Free Printable T3 Roots/Solutions/Zeros/X-Intercepts

1-12.

Answer the questions below after watching the video

1.

How can you find the factors of a polynomial if you know its solutions?

a)

By dividing the polynomial by the solutions

b)

By using the opposite sign of the solutions

c)

By multiplying the solutions

d)

By adding the solutions

2.

What does the factor theorem state?

a)

If x - a is a factor of f(x), then f(a) ≠ 0

b)

If f(a) = 0, then x - a is a factor of f(x)

c)

If f(x) = 0, then x is a factor of f(x)

d)

If f(x) is a polynomial, then x + a is a factor

3.

What is the first step in factorizing a cubic expression using the factor theorem?

a)

Find the derivative of the cubic

b)

Multiply the cubic by x

c)

Substitute a number to find a factor

d)

Divide the cubic by x

4.

What indicates that a number is a factor of a polynomial?

a)

When substituting it results in 0

b)

When substituting it results in -1

c)

When substituting it results in the number itself

d)

When substituting it results in 1

5.

What does the factor theorem help to identify in a polynomial?

a)

Its maximum value

b)

Its degree

c)

Its coefficients

d)

Its factors

6.

How can you verify if x + 5 is a factor of a polynomial?

a)

By substituting x = 5

b)

By substituting x = -5

c)

By multiplying the polynomial by x + 5

d)

By adding 5 to the polynomial

7.

How do you perform polynomial long division?

a)

By subtracting the divisor from the dividend

b)

By dividing each term of the polynomial by the divisor

c)

By multiplying the divisor by the quotient

d)

By dividing the highest degree term by x

8.

What does fully factorizing a cubic equation involve?

a)

Finding one factor and dividing the cubic by it

b)

Finding all linear factors only

c)

Finding all factors, including quadratic if present

d)

Solving the cubic equation for x

9.

What is the purpose of polynomial long division in the context of the factor theorem?

a)

To simplify the polynomial

b)

To find the derivative of the polynomial

c)

To multiply the polynomial by its factors

d)

To divide the polynomial by one of its factors

10.

How do you find the correct substitution for a factor like 2x + 1?

a)

By multiplying the factor by 2

b)

By setting 2x + 1 = 0 and solving for x

c)

By adding 1 to both sides of the equation

d)

By substituting x = 1 directly

11.

What modification is made to the factor theorem for factors like ax + b?

a)

If f(b/a) = 0, then ax + b is a factor

b)

If f(a/b) = 0, then ax - b is a factor

c)

If f(b/a) = 0, then ax - b is a factor

d)

No modification is needed

12.

What is the solution for x when 2x + 1 is set to 0?

a)

x = 0.5

b)

x = -0.5

c)

x = 1

d)

x = -1

13.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

14.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

15.

How many roots are shown in the picture?

a)

0

b)

1

c)

2

d)

3

16.

Zero: x = 9

What is the factor?

a)

(x - 9)

b)

(x + 9)

c)

9

d)

-9

17.

Zeros: x = 3 and x = 4

What are the factors?

a)

(x - 3)(x - 4)

b)

(x + 3)(x - 4)

c)

(x - 3)(x + 4)

d)

(x + 3)(x + 4)

18.

Zeros: x = -4 and x = -6

What are the factors?

a)

(x - 4)(x - 6)

b)

(x + 4)(x - 6)

c)

(x - 4)(x + 6)

d)

(x + 4)(x + 6)

19.

Zeros: x = 4 and x = -8

What are the factors?

a)

(x - 4)(x - 8)

b)

(x + 4)(x - 8)

c)

(x - 4)(x + 8)

d)

(x + 4)(x + 8)

20.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

21.

Find the zeros of the function and graph.
y=(x + 2)(x - 3)(3x - 5)

a)

x=-2, x=3, x=5/3

b)

x=2, x=-3, x=-3/5

c)

x=2, x=-3, x=5/3

d)

x=-2, x=3, x=5

22.

Which of the following shows the correct set up to prove that an x-intercept is a solution?

f\left(x\right)\ =\ x^2+2x-3

a)

$\left(-3\right)^2+2\left(-3\right)-3\ and\ \left(1\right)^2+2\left(1\right)-3$

b)

$\left(3\right)^2+2\left(3\right)-3\ and\ \left(-1\right)^2+2\left(-1\right)-3$

c)

$\left(-3\right)^2+2\left(-3\right)-3\ and\ \left(-1\right)^2+2\left(-1\right)-3$

d)

$\left(3\right)^2+2\left(3\right)-3\ and\ \left(1\right)^2+2\left(1\right)-3$

23.

If x = 5 and x = -3 are solutions of a polynomial, what are the factors?

a)

(x + 5)(x + 3)

b)

(x - 5)(x - 3)

c)

(x + 5)(x - 3)

d)

(x - 5)(x + 3)

24.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

25.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

26.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

27.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

28.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

29.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor!

b)

No, it is not a factor!

30.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

31.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

a)

Yes

b)

No

32.

Is (x-7) a factor of (x²-5x+14)?

a)

Yes

b)

No

33.

When (9x⁴- 45x³+ 37x² + x +2) is divided by (x-2), find the remainder.

a)

656

b)

652

c)

-64

d)

-368

34.

If P( -4) = 0, which of the following statements is true about P(x)?

a)

x+4 is a factor of P(x)

b)

P(x) = 0, has four negative roots

c)

4 is a root of P(x) = 0

d)

P(0) = - 4

35.

Given P(x) = 2x⁴ + x³ –3x² – x – 15. What is the value of P(2).

a)

25

b)

17

c)

11

d)

9

36.

(x – r) is a factor of P(x) if and only if __________.

a)

P(r) ≠ 0

b)

P(r) = 1

c)

P(r) = 0

d)

P(r) has two negative roots

37.

Is (y + 3) a factor of the polynomial: y³ - 6y + 9

a)

yes

b)

no

c)

maybe

d)

only on Tuesday's

38.

Find the remainder when

P\left(x\right)=x^4+x^3-2x^2+4x-5

is divided by

\left(x+3\right)

.

a)

19

b)

20

c)

21

d)

22

39.

Determine if $\left(x-1\right)$ is a factor of $5x^4-2x^3+3x-6$ .

a)

Yes

b)

No

40.

Determine if $\left(x-1\right)$ is a factor of $6x^3-2x^2+5x-8$ .

a)

Yes

b)

No

41.

What can we say if $P\left(-3\right)=0$ ?

a)

$\left(x-3\right)\$ is a factor of $P\left(x\right)$

b)

$\left(x+3\right)$ is a factor of $P\left(x\right)$

c)

$\left(x-3\right)$ is NOT a factor of $P\left(x\right)$

42.

What can we say if $P\left(2\right)=3$ ?

a)

$\left(x-2\right)$ is a factor of $P\left(x\right)$

b)

$\left(x-2\right)$ is NOT a factor of $P\left(x\right)$

c)

$\left(x+2\right)$ is NOT a factor of $P\left(x\right)$

43.

2n³ + 7n² - 2n - 7

a)

cannot be factored

b)

(n - 1)²(2n + 7)

c)

(n² - 1)(2n + 7)

d)

(n + 1)(n - 1)(2n + 7)

44.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

45.

Factor
x² - 4

a)

(x-2)²

b)

(x - 2)(x + 2)

c)

x(x - 4)

d)

2x(x - 2)

46.

Factor completely given (x-4) is a factor.
x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x -2)(x + 2)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

47.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor

b)

No, it is not a factor

48.

Factor by GCF:
17xy - x

a)

17(xy - x)

b)

y(17x - x)

c)

x(17y - 1)

d)

not factorable

49.

Factor completely
k²+7x+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

50.

One root of 2x³-13x²+36 is 2.
What is another zero?

a)

3/2

b)

6

c)

2

d)

-6

51.

How many possible roots does 2x³ + 8x² + 3x + 9 = 0 have based on the rational zero theorem?

a)

3 possible roots

b)

6 possible roots

c)

12 possible roots

d)

24 possible roots

52.

What are the roots of the following factored polynomial?
(x+1)(x-1)(2x+1)=0

a)

x= -1/2, -1, 1

b)

x= 1/2, -1, 1

c)

x = - ± 1

d)

x= 1/2, 1

53.

Which is not a factor of

a)

(x-1)

b)

(x+2)

c)

(x-4)

d)

(x+3)

54.

Describe how to create a list of rational zeros based on the Rational Root Theorem.

a)

Find the factors of the constant and factor it then divide it by the factors of the leading coefficient

b)

Factor all of the coefficients and divide them

c)

List all of the factors for the constant

d)

List all of the factors for the leading coefficient

55.

The polynomial is...

a)

Odd degree, positive leading coefficient.

b)

Odd degree, negative leading coefficient.

c)

Even degree, positive leading coefficient.

d)

Even degree, negative leading coefficient.

56.

Identify the zeros:

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

57.

Solve by quadratic formula
5x²-10x-40=0

a)

4,-2

b)

(-5±√103)/12

c)

(-5±√337)/12

d)

1±i√7

58.

The degree of the polynomial determines the max number of roots.

a)

True

b)

False

59.

The Rational Zeros Theorem states $\frac{p}{q}$ is a rational zero of $f\left(x\right)$ if $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient .

Is -3 a possible rational zero for the polynomial $f\left(x\right)$ ?

$f\left(x\right)=3x^3+2x^2-5x+2$

Why or why not?

a)

Yes, because 3 is a factor of p, the constant term of the polynomial.

b)

Yes, because 3 is a factor of q, the leading coefficient.

c)

No, because 3 is not a factor of p, the constant term of the polynomial.

d)

No, because 3 is not a factor of p, the constant term of the polynomial.

60.

Using the Rational Zeros Theorem, which is the complete list of the possible rational zeros for the polynomial function?

$f\left(x\right)=\ 2x^5+x^3-16$

a)

$\pm2,\ \pm4,\ \pm8$

b)

$\pm1,\pm2,\pm4,\pm8,\pm16$

c)

$\pm\frac{1}{4}\pm\frac{1}{2}\pm1,\pm2,\pm4,\ \pm8$

d)

$\pm\frac{1}{2}\pm1,\pm2,\pm4,\pm8,\pm16$

61.

Select 2 ways you can tell if $x-2$ is a factor of a polynomial function $f\left(x\right)$ .

a)

Substitute -2 for x in $f\left(x\right)$ to see if the end result is 0.

b)

Substitute 2 for x in undefinedto see if the end result is 0.

c)

Synthetically divide undefined by -2 to see if the end result is zero.

d)

Synthetically divide undefined by 2 to see if the end result is zero.

62.

Select 2 of the following statements that imply a zero of a polynomial function could have a multiplicity 4?

a)

The polynomials' graph has a bounce at the x intercept.

b)

One of the polynomials' factors has an exponent of 4.
Example: $\left(x-1\right)^4$

c)

The highest degree of the polynomial is 4.

d)

The polynomials' graph crosses the x- axis..

63.

What are the maximum number of real solutions the polynomial function could have?

$f\left(x\right)=-4x^5-4x^3-4x^2-4$

a)

5

b)

4

c)

3

d)

2

64.

Select 2 of the following statements that explain if $\left(x+2\right)$ is a factor of $f\left(x\right)=\ x^2+3x+7$ and why or why not.

a)

Yes, the function has a remainder of 0 when I synthetically divide by -2.

b)

Yes, because the function equals 0 when I substitute -2 in for x.

c)

No, the function has a remainder of 5 when I synthetically divide by -2

d)

No, because the function equals 5 when I substitute -2 in for x.

65.

When synthetically dividing $f\left(x\right)=-8x^4+x^2-5x^6$
by some factor of x, how must I list my coefficients?

a)

-8, 1, -5

b)

-5, -8, 1

c)

-8, 0, 1, -5, 0, 0

d)

-5, 0, -8, 0, 1, 0, 0

66.

What is a list of all the possible rational roots of the polynomial function?

$f\left(x\right)=\ x^3-4x^2+5x-12$

a)

$\pm1,\ \pm2,\pm3,\pm4,\pm6,\pm12$

b)

$\pm\frac{1}{2},\pm1,\ \pm2,\pm3,\pm4,\pm6,\pm12$

c)

$\pm\frac{1}{2},\pm\frac{3}{4}\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$

d)

$\pm\frac{1}{12},\pm\frac{1}{2},\pm\frac{3}{4}\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$

67.

Find all zeros for the polynomial function given one of the factors of the function is (x+3).

$f\left(x\right)=2x^3+5x^2-6x-9$

a)

$x=-3,-1$

b)

$x=-3,\ -1,\ \frac{3}{2}$

c)

$x=1,\ 3$

d)

$x=\ \frac{-3}{2},\ 1,\ 3,\$

68.

Which statement is NOT TRUE regarding the graphed polynomial function?

Check all that apply.

a)

The factors are $\left(x+1\right)\left(x-1\right)^2\left(x-2\right)$

b)

The factors areundefined

c)

The solutions are:
-2 (multiplicity of 1)
-1 (multiplicity of 2)
1 (multiplicity of 1)

d)

The intercepts are

(-1, 0), (0, 1), (1, 0), (2, 0)

69.

The Rational Zeros Theorem states undefined is a rational zero of undefined if undefined is a factor of the constant term and undefined is a factor of the leading coefficient . Is -2 a possible rational zero for the polynomial undefined? $f\left(x\right)=3x^3+2x^2-5x+2$ Why or why not?

a)

Yes, because 2 is a factor of p, the constant term of the polynomial.

b)

Yes, because 2 is a factor of q, the leading coefficient.

c)

No, because 2 is not a factor of p, the constant term of the polynomial.

d)

No, because 2 is not a factor of p, the constant term of the polynomial.

70.

The degree of the function is...

a)

the size of it

b)

the number of terms

c)

the greatest exponent on the variable

d)

How hot the function is

71.

What is the degree of $f\left(x\right)=\left(x+3\right)\left(x^2-4\right)$ ?

a)

3

b)

4

c)

1

d)

2

72.

Use the Fundamental Theorem of Algebra to determine the total number of REAL and IMAGINARY roots

$f\left(x\right)=x^8-17x^4+10x$

a)

4

b)

3

c)

8

d)

27

73.

Use the Fundamental Theorem of Algebra to determine the total number of REAL and IMAGINARY roots

$f\left(x\right)=8x^6+5x^2+23$

a)

6

b)

8

c)

23

d)

4

74.

Find the roots of the function: $f\left(x\right)=x\left(x+5\right)\left(x-7\right)$

$x=\$ type roots in the order of the problem above

(a)

75.

Find the roots of the function: $f\left(x\right)=x\left(2x-3\right)\left(5x-4\right)$

a)

$x=\frac{3}{2},\ \frac{4}{5}$

b)

$x=0,-\frac{3}{2},\ -\frac{4}{5}$

c)

$x=-\frac{3}{2},\ -\frac{4}{5}$

d)

$x=0,\frac{3}{2},\ \frac{4}{5}$

76.

Find the roots of the function: $f\left(x\right)=4x^3-5x^2-6x$

a)

$x=-\frac{3}{4},\ 2$

b)

$x=0,-\frac{3}{4},\ 2$

c)

$x=\frac{3}{4},-\ 2$

d)

$x=0,\frac{3}{4},\ -2$

77.

Find the roots of the function: $f\left(x\right)=4x^3+8x^2-9x-18$

a)

$x=-\frac{3}{2},\frac{3}{2},-\ 2$

b)

$x=-\frac{3}{2},\frac{3}{2},\ 2$

c)

$x=-\frac{2}{3},\frac{2}{3},-\ 2$

d)

$x=-\frac{2}{3},\frac{2}{3},\ 2$

78.

Find all of the factors and roots for the following function:

$\left(x+3\right)$ is a factor of the function $f\left(x\right)=3x^3+14x^2+13x-6$

a)

$x=-3,2,3$

b)

$x=x=-3,-2,-\frac{1}{3}$

c)

$x=-3,-2,3$

d)

$x=-3,-2,\frac{1}{3}$

79.

Write a polynomial function with a leading coefficient of -5 and roots of 3, -4 and 7

Factored Form

$f\left(x\right)=$ write your answer in order of the given information

(a)

80.

Write a polynomial function with a leading coefficient of -5 and roots of 3, -4 and 7

Standard Form

a)

$f\left(x\right)=x^3-6x^2-19x+84$

b)

$f\left(x\right)=-5x^3+30x^2+95x-420$

c)

$f\left(x\right)=-5x^3-6x^2-19x+84$

d)

$f\left(x\right)=x^2-3x-28$

81.

Write a polynomial function with a leading coefficient of 2 and roots of -3, 7i

Factored Form

a)

$f\left(x\right)=2\left(x+3\right)\left(x-7i\right)$

b)

$f\left(x\right)=2\left(x-3\right)\left(x-7i\right)$

c)

$f\left(x\right)=2\left(x+3\right)\left(x-7i\right)\left(x+7i\right)$

d)

$f\left(x\right)=2\left(x-3\right)\left(x-7i\right)\left(x+7i\right)$

82.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

83.

Is (x-4) a factor of (x³ +x² -16x-16)?

a)

YES

b)

NO

84.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x-12

b)

2x⁴-x³-25x²-12x+0

85.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

86.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

87.

Decide if (x-3) is a factor of 3x³+10x²-x-12

a)

Yes, it is a factor!

b)

No, it is not a factor!

88.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

89.

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

a)

Yes

b)

No

90.

Is (x-7) a factor of (x²-5x+14)?

a)

Yes

b)

No

91.

When (9x⁴- 45x³+ 37x² + x +2) is divided by (x-2), find the remainder.

a)

656

b)

652

c)

-64

d)

-368

92.

If P( -4) = 0, which of the following statements is true about P(x)?

a)

x+4 is a factor of P(x)

b)

P(x) = 0, has four negative roots

c)

4 is a root of P(x) = 0

d)

P(0) = - 4

93.

Given P(x) = 2x⁴ + x³ –3x² – x – 15. What is the value of P(2).

a)

25

b)

17

c)

11

d)

9

94.

(x – r) is a factor of P(x) if and only if __________.

a)

P(r) ≠ 0

b)

P(r) = 1

c)

P(r) = 0

d)

P(r) has two negative roots

95.

Is (y + 3) a factor of the polynomial: y³ - 6y + 9

a)

yes

b)

no

c)

maybe

d)

only on Tuesday's

96.

Find the remainder when

P\left(x\right)=x^4+x^3-2x^2+4x-5

is divided by

\left(x+3\right)

.

a)

19

b)

20

c)

21

d)

22

97.

Determine if $\left(x-1\right)$ is a factor of $5x^4-2x^3+3x-6$ .

a)

Yes

b)

No

98.

Determine if $\left(x-1\right)$ is a factor of $6x^3-2x^2+5x-8$ .

a)

Yes

b)

No

99.

What can we say if $P\left(-3\right)=0$ ?

a)

$\left(x-3\right)\$ is a factor of $P\left(x\right)$

b)

$\left(x+3\right)$ is a factor of $P\left(x\right)$

c)

$\left(x-3\right)$ is NOT a factor of $P\left(x\right)$

100.

What can we say if $P\left(2\right)=3$ ?

a)

$\left(x-2\right)$ is a factor of $P\left(x\right)$

b)

$\left(x-2\right)$ is NOT a factor of $P\left(x\right)$

c)

$\left(x+2\right)$ is NOT a factor of $P\left(x\right)$

101.

The degree of the polynomial determines the max number of roots.

a)

True

b)

False

102.

The Rational Zeros Theorem states $\frac{p}{q}$ is a rational zero of $f\left(x\right)$ if $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient .

Is -3 a possible rational zero for the polynomial $f\left(x\right)$ ?

$f\left(x\right)=3x^3+2x^2-5x+2$

Why or why not?

a)

Yes, because 3 is a factor of p, the constant term of the polynomial.

b)

Yes, because 3 is a factor of q, the leading coefficient.

c)

No, because 3 is not a factor of p, the constant term of the polynomial.

d)

No, because 3 is not a factor of p, the constant term of the polynomial.

103.

Using the Rational Zeros Theorem, which is the complete list of the possible rational zeros for the polynomial function?

$f\left(x\right)=\ 2x^5+x^3-16$

a)

$\pm2,\ \pm4,\ \pm8$

b)

$\pm1,\pm2,\pm4,\pm8,\pm16$

c)

$\pm\frac{1}{4}\pm\frac{1}{2}\pm1,\pm2,\pm4,\ \pm8$

d)

$\pm\frac{1}{2}\pm1,\pm2,\pm4,\pm8,\pm16$

104.

Select 2 ways you can tell if $x-2$ is a factor of a polynomial function $f\left(x\right)$ .

a)

Substitute -2 for x in $f\left(x\right)$ to see if the end result is 0.

b)

Substitute 2 for x in undefinedto see if the end result is 0.

c)

Synthetically divide undefined by -2 to see if the end result is zero.

d)

Synthetically divide undefined by 2 to see if the end result is zero.

105.

Select 2 of the following statements that imply a zero of a polynomial function could have a multiplicity 4?

a)

The polynomials' graph has a bounce at the x intercept.

b)

One of the polynomials' factors has an exponent of 4.
Example: $\left(x-1\right)^4$

c)

The highest degree of the polynomial is 4.

d)

The polynomials' graph crosses the x- axis..

106.

What are the maximum number of real solutions the polynomial function could have?

$f\left(x\right)=-4x^5-4x^3-4x^2-4$

a)

5

b)

4

c)

3

d)

2

107.

Select 2 of the following statements that explain if $\left(x+2\right)$ is a factor of $f\left(x\right)=\ x^2+3x+7$ and why or why not.

a)

Yes, the function has a remainder of 0 when I synthetically divide by -2.

b)

Yes, because the function equals 0 when I substitute -2 in for x.

c)

No, the function has a remainder of 5 when I synthetically divide by -2

d)

No, because the function equals 5 when I substitute -2 in for x.

108.

When synthetically dividing $f\left(x\right)=-8x^4+x^2-5x^6$
by some factor of x, how must I list my coefficients?

a)

-8, 1, -5

b)

-5, -8, 1

c)

-8, 0, 1, -5, 0, 0

d)

-5, 0, -8, 0, 1, 0, 0

109.

What is a list of all the possible rational roots of the polynomial function?

$f\left(x\right)=\ x^3-4x^2+5x-12$

a)

$\pm1,\ \pm2,\pm3,\pm4,\pm6,\pm12$

b)

$\pm\frac{1}{2},\pm1,\ \pm2,\pm3,\pm4,\pm6,\pm12$

c)

$\pm\frac{1}{2},\pm\frac{3}{4}\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$

d)

$\pm\frac{1}{12},\pm\frac{1}{2},\pm\frac{3}{4}\pm1,\pm2,\pm3,\pm4,\pm6,\pm12$

110.

Find all zeros for the polynomial function given one of the factors of the function is (x+3).

$f\left(x\right)=2x^3+5x^2-6x-9$

a)

$x=-3,-1$

b)

$x=-3,\ -1,\ \frac{3}{2}$

c)

$x=1,\ 3$

d)

$x=\ \frac{-3}{2},\ 1,\ 3,\$

111.

Which statement is NOT TRUE regarding the graphed polynomial function?

Check all that apply.

a)

The factors are $\left(x+1\right)\left(x-1\right)^2\left(x-2\right)$

b)

The factors areundefined

c)

The solutions are:
-2 (multiplicity of 1)
-1 (multiplicity of 2)
1 (multiplicity of 1)

d)

The intercepts are

(-1, 0), (0, 1), (1, 0), (2, 0)

112.

The Rational Zeros Theorem states undefined is a rational zero of undefined if undefined is a factor of the constant term and undefined is a factor of the leading coefficient . Is -2 a possible rational zero for the polynomial undefined? $f\left(x\right)=3x^3+2x^2-5x+2$ Why or why not?

a)

Yes, because 2 is a factor of p, the constant term of the polynomial.

b)

Yes, because 2 is a factor of q, the leading coefficient.

c)

No, because 2 is not a factor of p, the constant term of the polynomial.

d)

No, because 2 is not a factor of p, the constant term of the polynomial.

113.

Is (x – 2) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(2) = 0

b)

No, f(2) = 20

c)

Yes, f(2) = 20

d)

No, f(2) = 0

114.

Is (x + 3) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(-3) = 0

b)

No, f(-3) = 20

c)

Yes, f(3) = 0

d)

No, f(3) = 60

115.

Is (x - 1) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(1) = 0

b)

No, f(1) = -2

c)

Yes, f(-1) = 0

d)

No, f(-1) = -2

116.

Is (x + 1) a factor

$f\left(x\right)\ =\ x^3+4x^2\ +x\ -6$

a)

Yes f(-1) = 0

b)

No, f(-1) = -4

c)

Yes, f(1) = 0

d)

No, f(1) = -4

117.

Is (x - 2) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(2) = 0

b)

No, f(2) = 2

c)

Yes, f(-2) = 0

d)

No, f(-2) = -2

118.

Is (x + 3) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(3) = 0

b)

No, f(3) = 3

c)

Yes, f(-3) = 0

d)

No, f(-3) = -3

119.

Is (x - 1) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(1) = 0

b)

No, f(1) = 24

c)

Yes, f(-1) = 0

d)

No, f(-1) = 24

120.

Is (x + 1) a factor

$f\left(x\right)\ =\ x^4-13x^2\ +36$

a)

Yes f(1) = 0

b)

No, f(1) = 24

c)

Yes, f(-1) = 0

d)

No, f(-1) = 24

121.

Is (x - 2) a factor

$f\left(x\right)\ =\ x^3-x^2\ -9x+9$

a)

Yes f(2) = 0

b)

No, f(2) = -5

c)

Yes, f(-2) = 0

d)

No, f(-2) = -5

122.

Is (x - 3) a factor

$f\left(x\right)\ =\ x^3-x^2\ -9x+9$

a)

Yes f(3) = 0

b)

No, f(3) = -5

c)

Yes, f(-3) = 0

d)

No, f(-3) = -5

123.

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

a)

x + 1

b)

x + 2

c)

x + 5

d)

x + 10

124.

What is the remainder when a³ - 4 is divided by a+2?

a)

-2

b)

-6

c)

-12

d)

0

125.

Which binomial is a factor of
f(x)= x³ + x² -24x +36?

a)

x + 2

b)

x + 3

c)

x + 6

d)

x + 9

126.

Which binomial is a factor of
f(x)= 6x³ -35x² +34x +40?

a)

2x - 3

b)

2x - 5

c)

3x - 2

d)

5x - 2

127.

What is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

a)

-25

b)

25

c)

113

d)

-113

128.

What are the three factors for
(x³ -3x² -4x +12) ÷ (x + 2)?

a)

(x-2) (x+2) (x+3)

b)

(x-2) (x-2) (x+3)

c)

(x+2) (x+2) (x+3)

d)

(x-2) (x+2) (x-3)

129.

For division, what # is in the left
box?

a)

0

b)

1

c)

2

d)

3

130.

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division.

a)

0

b)

10

c)

15

d)

-7

131.

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

a)

p(2) = 656

b)

p(2) = 652

c)

p(2) = -64

d)

p(2) = -368

132.

What are the three factors for
(x³ +7x² +7x -15) ÷ (x -1)?

a)

(x-1) (x+5) (x-3)

b)

(x-1) (x+5) (x + 3)

c)

(x+1) (x+5) (x-3)

d)

(x+1) (x-5) (x-3)

133.

Which term is missing in this problem?
(2x³ + 5x² + 9) ÷
(x + 3)

a)

x⁴

b)

x³

c)

x²

d)

x

134.

Factor:
x²-16x + 48

a)

(x - 12)(x - 4)

b)

(x + 6)(x - 8)

c)

(x + 12)(x - 4)

d)

(x -16)(x - 3)

135.

Solve the equation by factoring:
x²-6x+8=0

a)

2, 4

b)

-2, -4

c)

-2, 4

d)

2, -4

136.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

137.

What is another name for the x-intercepts of a quadratic?

a)

y-intercepts

b)

zeros

c)

x-axis

d)

none of these

138.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

139.

What are the solutions?

a)

0 and 8

b)

-2 and -4

c)

3 and -1

d)

2 and 4

140.

a)

(x-1)(x+3)

b)

(x+1)(x-3)

c)

(x-1)(x-3)

d)

(x+1)(x+3)

141.

Which of the following is one of the roots of the function? f(x) = (x+3)(x-6)

a)

2

b)

-2

c)

-6

d)

-3

142.

Which of the following is a solution to the function? (x - 8)(x - 9) = 0

a)

8

b)

-9

c)

-17

d)

0

143.

Which is an x-intercept of the function?

a)

undefined

b)

1

c)

2

d)

-1

144.

How many solutions does the graph have?

a)

0

b)

1

c)

2

d)

3

145.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

146.

A quadratic function has zeros -7 and 9.
What are the linear factors of the function?

a)

(x+7) (x-9)

b)

(x-7) (x+9)

c)

(-7,0) (9,0)

d)

(0,-7) (0,9)

147.

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

1, -6, 5

148.

What is another word for zeros?

a)

solutions

b)

x -intercepts

c)

roots

d)

All of the these!

149.

(End Behavior): Find the end behavior of the polynomial $f\left(x\right)=-x^3+x^2+4x\ -8$

a)

b)

c)

d)

150.

(End Behavior): Find the end behavior of the polynomial $f\left(x\right)=\left(x+1\right)\left(x-3\right)\left(x+7\right)^2$

a)

b)

c)

d)

151.

(End Behavior): Find the end behavior of the graph

a)

b)

c)

d)

152.

(End Behavior): Find the end behavior of the graph

a)

b)

c)

d)

153.

(Graphing): Write an equation for the graph below

a)

$f\left(x\right)\ =\ \left(x+3\right)\left(x-2\right)^2\left(x-5\right)$

b)

$f\left(x\right)\ =\ -\left(x+3\right)\left(x-2\right)^2\left(x-5\right)$

c)

$f\left(x\right)\ =\ \left(x-3\right)\left(x+2\right)^2\left(x+5\right)$

d)

$f\left(x\right)\ =\ \left(x-3\right)^2\left(x+2\right)\left(x+5\right)$

154.

(Graphing): Write an equation for the graph below

a)

$f\left(x\right)\ =\ x\left(x+2\right)^2\left(x-2\right)$

b)

$f\left(x\right)\ =\ x\left(x+2\right)\left(x-2\right)$

c)

$f\left(x\right)\ =\ \left(x-2\right)\left(x+2\right)$

d)

$f\left(x\right)=-x\left(x+2\right)\left(x-2\right)$

155.

(Characteristics) Write the factored form equation for a polynomial with a degree of 3 and zeros at x = 1 and x = 3

a)

$f\left(x\right)\ =\ \left(x-1\right)\left(x-3\right)^2$

b)

$f\left(x\right)\ =\ \left(x-1\right)\left(x-3\right)$

c)

$f\left(x\right)\ =\ \left(x+1\right)\left(x+3\right)^2$

d)

$f\left(x\right)\ =\ \left(x+1\right)\left(x+3\right)$

156.

(Synthetic Division): Given the following work, what are the factors of the polynomial?

a)

(x-1)(x-2)(x-1)

b)

(x-1)(x+2)(x-1)

c)

(x+1)(x+2)(x-1)

d)

(x+1)(x-2)(x-1)

157.

(Factor Theorem): Using the factor theorem, which of the below is a true statement?

a)

(x+1) is a factor

b)

(x-1) is a factor

c)

(x+1) is not a factor

d)

x = 1 is a root

158.

(Remainder Theorem): Using the remainder theorem, which of the below is a true statement?

a)

(x-4) is a factor

b)

(x+4) is a factor

c)

(4,27) is a point on the graph

d)

(27,4) is a point on the graph

159.

(Factor Theorem): Using the factor theorem, which of the below is a true statement?

a)

(x+2) is a factor

b)

(x-2) is a factor

c)

(x-2) is not a factor

d)

x = -2 is a root

160.

(Remainder Theorem): Using the remainder theorem, which of the below is a true statement?

a)

f(12) = 1

b)

f(1) = 12

c)

(x+1) is a root

d)

(x-1) is a root

161.

(Rational Root Theorem): Find the possible roots of the polynomial $f\left(x\right)\ =\ x^3+3x^2\ -4x+12$

a)

$\pm1,\ \pm2,\ \pm3,\ \pm4,\ \pm6,\ \pm12$

b)

$\pm1,\ \pm2,\ \pm4$

c)

$\pm1,\ \pm2,\ \pm6,\ \pm12$

d)

$\pm\frac{1}{2},\ \pm1,\ \pm\frac{3}{2},\ \pm2$

162.

(Rational Root Theorem): Find the possible roots of the polynomial $f\left(x\right)\ =\ x^3+5x^2\ +3x+20$

a)

$\pm1,\ \pm2,\ \pm6,\ \pm20$

b)

$\pm1,\ \pm2,\ \pm4,\ \pm5,\ \pm10,\ \pm20$

c)

$\pm1,\ \pm2,\ \pm5,\ \pm15$

d)

$\pm\frac{1}{2},\ \pm1,\ \pm\frac{3}{2},\ \pm2$

163.

(Synthetic Division): Given the following work, what are the factors of the polynomial?

a)

(x-2)(x-4)(x+3)

b)

(x+2)(x-4)(x+3)

c)

(x+2)(x+4)(x+3)

d)

(x-2)(x-4)(x-3)

T3 Roots/Solutions/Zeros/X-Intercepts

Total questions: 152

Worksheet time: 11hrs 9mins

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