Free Printable 9th - 11th Final Exam

1.

Classify the following polynomial

(a)

2.

Classify the following polynomial

(a)

3.

Classify the following polynomial

a)

binomial polynomial

b)

quadratic binomial

c)

quartic binomial

4.

Classify the polynomial:
3x² – 8x + 1

(a)

5.

Is this expression in Standard Form?
6w² - 9w³

a)

Yes

b)

No

6.

What is the degree?
- 10x - 3x³ - x² + 12

(a)

7.

Describe the expression $2x^2+3x\ +2x\ =x^2$ by its number of terms.

a)

monomial

b)

binomial

c)

trinomial

d)

multinomial

(4 terms and above)

e)

Not a polynomial

8.

Describe the expression $5y^3+4y$ by its number of terms.

a)

monomial

b)

binomial

c)

trinomial

d)

multinomial

(4 terms and above)

e)

Not a polynomial

9.

If the expression $2x^2+3x$ is a polynomial, what is its degree?

a)

2

b)

1

c)

0

d)

Not a polynomial

10.

If the expression $5y^3+4y$ is a polynomial, what is its degree?

a)

2

b)

1

c)

0

d)

Not a polynomial

e)

3

11.

If the expression $x^{-2}+5x^{-1}+4$ is a polynomial, what is its degree?

a)

3

b)

0

c)

1

d)

Not a polynomial

e)

2

12.

If the expression $\frac{1}{2x^2-5x}$ is a polynomial, what is its degree?

a)

3

b)

0

c)

1

d)

Not a polynomial

e)

2

13.

If the expression $\frac{1}{6}n+\frac{1}{2}n^3+\frac{1}{3}n^2$ is a polynomial, what is its degree?

a)

1

b)

2

c)

3

d)

Not a polynomial

e)

0

14.

Classify by degree of polynomial:
3x³ – 6x - 2x + 5x³

(a)

15.

Classify by degree of polynomial:
2x – 9

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

16.

The following polynomial is written in standard form:
7x³ - 11x² + 8x - 5

a)

True

b)

False

17.

Simplify into Standard Form:

$4x^2-5x+10+2x^2\ +12x\ -3$

a)

$6x^2+7x\ +8$

b)

$6x^2+7x\ +7$

c)

$11x^2+7$

d)

$7$

18.

Put in Standard Form.
12 - 3x³ - 10x - x²

a)

- 3x³ - x² - 10x + 12

b)

3x³ - x² + 10x + 12

c)

12 - 3x³ - 10x - x²

d)

12 - 10x - 3x³ - x²

19.

Reorder the following polynomial into Standard Form

$-x^2-15x+7x^4-6+3x^3$

a)

$+7x^4$

b)

$+3x^3$

c)

$-x^2$

d)

$-15x$

e)

$-6$

1)

2)

3)

4)

5)

20.

The largest exponent which is shown in a polynomial.

a)

exponent

b)

cubic

c)

degree

d)

linear

21.

What is the value of the constant?
2x² + 4x − 5

a)

2

b)

4

c)

5

d)

−5

22.

Which algebraic expressions are polynomials?

a)

$\pi x-\sqrt{3}+5y$

b)

$x^2y^2-4x^3+12y$

c)

$\frac{4}{x}-x^2$

d)

$\sqrt{x}-16$

e)

$3.9x^3-4.1x^2+7.3$

23.

Which polynomial is written in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

24.

Which of these is in Standard Form?

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+5x-9$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

25.

Match the following.

a)

Add the exponents

1.

$x^3\cdot x^6$

b)

Subtract the exponents

2.

$\frac{z^8}{z^4}$

c)

Multiply the exponents

3.

$\left(y^2\right)^4$

26.

Match the following.

a)

Add the exponents

1.

$\left(w^2\right)^2$

b)

Subtract the exponents

2.

$v^3\cdot v^5$

c)

Multiply the exponents

3.

$\frac{b^2}{b^4}$

27.

(c⁵)(c³)(c³)

a)

c⁴⁵

b)

3c¹¹

c)

c¹¹

d)

3c⁴⁵

28.

Put the terms of the polynomial in Standard Form

a)

$2x^5$

b)

$-3x^3$

c)

$x^2$

d)

$-7x$

e)

$6$

1)

2)

3)

4)

5)

29.

Which of the following is a quadratic binomial when simplified ?

a)

$6x^2+5x-2$

b)

$5x+9x^2-5x$

c)

$13-4x^2+7x-13$

d)

$7x-12-3x^2-2x^3$

30.

Select the TWO statements that are true about the expression below.

$-4x^3+6x^2-7$

a)

The polynomial is a cubic trinomial

b)

The leading coefficient is 4

c)

The polynomial is a quartic trinomial

d)

The leading coeeficient is -4

e)

The polynomial is not in standard form

31.

Classify the monomial below.

$3x^4y+2x^2+2xy+2$

(a)

32.

What is the leading coefficient of the polynomial below?

$2x^4+8x-3x^7+6$

(a)

33.

Match the simplified version of the polynomial with it's classification.

a)

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

1.

Cubic Binomial

b)

$\left(x^4-8x^3+2\right)+\left(-3x^3-x+5x^4\right)$

2.

Quartic Polynomial

c)

$\left(x^3-3x+6\right)+\left(5x-x^3-6\right)$

3.

Linear Monomial

d)

$\left(7-x^2+4x+2x^3\right)+\left(4-2x^2-2x^3+4x\right)$

4.

Quadratic Trinomial

34.

The sum of two binomials is $8x-13$ . If one of the trinomials is $-3x^2+7x-2$ , what is the other trinomial?

$\left(-3x^2+7x-2\right)+$ ____________ $=8x-13$

a)

$3x^2+x+11$

b)

$-3x^2-x-11$

c)

$3x^2+x-11$

d)

$-3x^2+x+11$

35.

Which of the following is a cubic polynomial?

a)

$3x^2+x^2+2x+1$

b)

$3x^3-x^2+2x^3+x+3x+2$

c)

$-x + 4$

d)

$4x^4-3x^2+2x+2$

36.

Match the following

a)

1.

Trinomial

b)

2.

Mononomial

c)

3.

Binomial

d)

4.

Polynomial with 6 terms

e)

5.

Polynomial with 5 terms

37.

Describe the types of Polynomials for each polynomial

a)

(6x + 9)

1.

binomials

b)

$x^2+5x-2$

2.

trinomials

c)

2x

3.

monomials

d)

$4x^2\ +6x^4-3x+5-2x^7$

4.

polynomial

38.

Find the sum.
(3 - 2x + 2x²) + (4x - 5 + 3x²)

a)

7x - 7x + 5x²

b)

5x²+ 2x - 2

c)

5x²

d)

5x² + 6x + 8

39.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

40.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

41.

How many terms does the polynomial have?

$2ab^2-4c+6d^3-12ef\ +\ 101$

42.

Rewrite $2x^2+9-5x^3+3x^4-8x$ in standard form.

a)

$+3x^4$

b)

$-5x^3$

c)

$+2x^2$

d)

$-8x$

e)

$9$

1)

2)

3)

4)

5)

43.

What is the lead coefficient of the polynomial?

$-4a^3+19a^4-a+12a^6+103$

44.

In the example

$5v^3-7$ the constant is:

(a)

45.

How many terms are in the polynomial

$3x^2+4x-8$

(a)

46.

According to exponent rules, when we multiply terms with the same base we _______ the exponents.

a)

Multiply

b)

Add

c)

Divide

d)

Subtract

47.

Simplify:

$5\left(3x+2\right)$

a)

$3x+10$

b)

$15x+10$

c)

$15x-10$

d)

$3x-10$

48.

When SUBTRACTING polynomials, remember:

1 - Match Up

2 - Flip the signs of 2nd Polynomial

3 - Combine

( 5x² + 8x + 7 ) - ( 2x² + 2x + 2 )

a)

7x² + 10x + 8

b)

-3x² - 6x - 5

c)

3x² + 6x + 5

49.

Add the polynomial (-3x + 4) + (8x - 5)

a)

5x - 9

b)

5x - 1

c)

11x - 1

d)

11x - 9

e)

None of these

50.

Put the terms in Standard Order. (List the exponents from highest to lowest.)

a)

x⁸

b)

7x⁵

c)

8x⁴

d)

12x²

e)

x

1)

2)

3)

4)

5)

51.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

52.

Which equation MOST LIKELY matches the graph?

a)

y = x⁴- x³ + 3x² + 2

b)

y = -x⁴ + x³ + 5x + 2

c)

y = x³ - 2x² + 1x + 3

d)

y = -x³ - 2x² + 1x + 3

53.

Based on the end behavior of the polynomial, what best describes the leading coefficient?

a)

a negative real number

b)

a positive real number

c)

an even real number

d)

an odd real number

54.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

55.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

56.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

57.

What is the degree?

a)

Positive

b)

Negative

c)

Even

d)

Odd

58.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

59.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

60.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

61.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

62.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Even

d)

Odd

63.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

64.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

65.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

66.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

67.

Describe the end behavior of the function.
y = 4x¹⁰

a)

down and down

b)

down and up

c)

up and down

d)

up and up

68.

Describe the end behavior of the function. (Put the polynomial in standard form first*)
y = -6x + 4 + 9x³

a)

down and down

b)

down and up

c)

up and down

d)

up and up

69.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

70.

f(x) = 4 + 3x - 6x⁷ + 3x⁴

a)

UP and UP

b)

DOWN and DOWN

c)

UP and DOWN

d)

DOWN and UP

71.

Is $y=\sqrt{x^3-7x^2+8x-1}$ a polynomial?

a)

Yes, with degree 3 and leading coefficient 1.

b)

No, this is a square root of a polynomial, but not a polynomial.

72.

Match the following:

a)

Monomial

1.

( $-2x$ )

b)

Binomial

2.

( $3x^2+7$ )

c)

Trinomial

3.

( $5x^2+7x-10$ )

d)

Polynomial

4.

( $8x^4+7x^2+3x-9$ )

73.

Describe the types of Polynomials for each polynomial

a)

(6x + 9)

1.

binomials

b)

$x^2+5x-2$

2.

trinomials

c)

2x

3.

monomials

d)

$4x^2\ +6x^4-3x+5-2x^7$

4.

polynomial

74.

What is the degree of the function graphed here?

a)

2

b)

3

c)

4

d)

5

75.

Fill in the blank with the correct term.

(You must spell the answer correctly or you may get the answer wrong. Make sure to look back at your notes.)

(a) - a number without a variable

76.

Fill in the blank with the correct term.

(You must spell the answer correctly or you may get the answer wrong. Make sure to look back at your notes.)

(a) - the parts of the polynomial that are separated by + or - signs

77.

Fill in the blank with the correct term.

(You must spell the answer correctly or you may get the answer wrong. Make sure to look back at your notes.)

(a) - a letter used to represent unknown values

78.

Fill in the blank with the correct term.

(You must spell the answer correctly or you may get the answer wrong. Make sure to look back at your notes.)

(a) - the number being multiplied by a variable

79.

Simplify the expression.
(4a³ - 8a - 4a²) + (7a³ - 7 - 6a)

a)

11a³ - 4a² - 14a - 7

b)

5a³ - 4a² - 14a - 7

c)

5a³ - 4a² - 20a - 7

d)

5a³ - 9a² - 20a - 7

80.

(x³-x²+4) - (3x³-2x²+3)

a)

-2x³-3x²+7

b)

-2x³+x²+1

c)

2x³-3x³-1

d)

4x³-3x²+7

81.

The number in front of the variable is called the....

a)

exponent

b)

base

c)

coefficient

d)

fronter

82.

What are like terms?
Terms that have....

a)

the same variables

b)

the same exponents

c)

the same coefficients

d)

the same variables and exponents

83.

Classify by number of terms:
12

a)

Monomial

b)

Binomial

c)

Trinomial

d)

4-Term Polynomial

84.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Linear

Quadratic

Cubic

4th dgree

5th degree

Monomial

Binomial

Trinomial

Polynomial

85.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Quadratic

Cubic

4th dgree

5th degree

Monomial

Binomial

Trinomial

Polynomial

86.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Cubic

4th dgree

5th degree

Monomial

Trinomial

Polynomial

Linear

87.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Cubic

4th dgree

5th degree

Polynomial

Monomial

Linear

Quadratic

Binomial

Trinomial

88.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Cubic

5th degree

Monomial

4th degree

Binomial

Linear

Trinomial

Polynomial

Quadratic

89.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Cubic

4th dgree

5th degree

Monomial

Linear

Quadratic

Binomial

Trinomial

Polynomial

90.

The name of the polynomial is (a) (b)

Choose from the below words

Constant

Cubic

4th dgree

5th degree

Trinomial

91.

(a) (b)

Choose from the below words

Cubic

Monomial

Constant

Linear

Quadratic

4th degree

5th degree

Binomial

Trinomial

Polynomial

92.

(a) (b)

Choose from the below words

Constant

Linear

Quadratic

4th degree

5th degree

Binomial

Trinomial

Polynomial

93.

(a) (b)

Choose from the below words

Constant

Linear

4th degree

5th degree

Trinomial

Polynomial

Monomial

Binomial

Quadratic

Cubic

94.

(a) (b)

Choose from the below words

Constant

Linear

5th degree

Polynomial

Monomial

Binomial

Quadratic

Cubic

4th degree

Trinomial

95.

(a) (b)

Choose from the below words

Constant

5th degree

Polynomial

Monomial

Quadratic

Cubic

4th degree

Trinomial

Linear

Binomial

96.

(a) (b)

Choose from the below words

Constant

5th degree

Monomial

Quadratic

4th degree

Trinomial

Linear

Binomial

Cubic

Polynomial

97.

(a) (b)

Choose from the below words

Constant

5th degree

Monomial

4th degree

Linear

Binomial

Cubic

Polynomial

Trinomial

Quadratic

98.

(a) (b)

Choose from the below words

Constant

5th degree

Monomial

Quartic

Linear

Binomial

Polynomial

Quadratic

Cubic

Trinomial

99.

(a) (b)

Choose from the below words

Constant

5th degree

Monomial

Linear

Polynomial

Quadratic

Cubic

Trinomial

4th degree

Binomial

100.

Classify the Polynomial $3x^7+3x+2$

(a)

101.

$4xy$

Classify by degree.

a)

Constant

b)

Linear

c)

Quadratic

d)

Cubic

e)

5th Degree

102.

Name the following $3x^2-5x^4+3x+4x^3$

(a)

103.

Find the zeros of the polynomial.
f(x) = (x-5)(2x+3)(7x-4)(x+6)

a)

x = 5, (2/3), 6, (7/4)

b)

x= -5, (3/2), (-4/7), 6

c)

x= 5, (-3/2), (4/7), -6

d)

x= 6, 5, -2/3, -4/7

104.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

105.

What do "zeros" represent?

a)

something a polynomial can not be.

b)

the place that the polynomial crosses the x axis/ the x value that makes the whole equation equal to zero

c)

the place that the polynomial crosses the y axis/ the y value where x=0

d)

the number zero

106.

To find zeroes of polynomials, we...

a)

say x=0

b)

make pancakes

c)

ask NASA

d)

set factors equal to zero

107.

Note that:

x^2+4x-5=\left(x+5\right)\left(x-1\right)

What are the factors of

x^2+4x-5

?

(a)

108.

For $\left(x+5\right)\left(x-1\right)=0$ , what is x equal to? (You can only select 1 answer!!!)

a)

x=-5

b)

x=-4 x=1

c)

x=1

d)

x=1 and x=-5

e)

x=-1 and x=5

109.

The degree of the function is...

a)

the size of it

b)

the number of terms

c)

the greatest exponent on the variable

d)

a BS in mathematics

110.

The degree of a function is always equal to...

a)

the number of petals on a daisy

b)

the number of factors

c)

one less than the number of zeros

d)

the number of terms in the polynomial

111.

Even Multiplicities have which of the following effects on the x-axis?

a)

touches and bounces back

b)

wiggle

c)

crosses the x-axis

112.

Which zero has an odd multiplicity?

a)

-4

b)

4

c)

2

d)

-2

113.

Which root has even multiplicity?

a)

1

b)

-4

c)

-1

d)

2

114.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

115.

What is the Degree of this polynomial:
f(x)= x³(x + 3)²(x – 5)

a)

Degree: 6

b)

Degree: 5

c)

Degree: 3

d)

Degree: 2

116.

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

a)

{0 mult. 3, 5, 2}

b)

{−2 mult. 3, 3, 1}

c)

{0 mult. 3, 3, 2}

d)

{2 mult. 3, 3, 3}

117.

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

a)

{0 mult. 3}

b)

{0, 3, 1}

c)

{0, −2, −1}

d)

{−2, 3, 1}

118.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

119.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

120.

What are the roots of the polynomial function?
y = 9(x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 0

c)

9, 2, -7 multiplicity 3

d)

2, -7, 3

121.

State the zeros of the polynomial (include multiplicity):
f(x) = x⁴(x+3)²(x - 2)

a)

0, 3, 2

b)

0(multiplicity of 4), -3 (multiplicity of 2), 2

c)

-3 (multiplicity of 2), 2

d)

0, 2 (multiplicity of 3)

122.

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

a)

0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

b)

2 (Mult of 3), 7 (mult 1)

c)

0, 2, 7

d)

2 (mult of 2), 7 (mult of 3)

123.

Select polynomial whose zeros and degree are given.
Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4.

a)

(x + 5)³(x - 9)²(x + 2)(x - 4)

b)

(x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

c)

(x + 5)³(x - 9)²(x + 2)

d)

(x + 5)(x - 9)(x + 2)(x - 4)

124.

Odd Multiplicities have which of the following effects on the x-axis?

a)

Cross the x-axis

b)

Turn on the x-axis

125.

Find the zeros.

(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

126.

Find the zeros.

(2x - 1)(x + 4) = 0

a)

{ 1/2, -4 }

b)

{ 1/2, 4 }

c)

{ 2, -4 }

d)

{ -2, 4 }

127.

Solve and find your x-intercepts:
0=x(x - 6)

a)

x=0 and x=-6

b)

x=1 and x=-6

c)

x=0 and x=6

d)

x=6

128.

Solve by grouping.

12x(x + 2) + 2x + 4

a)

(12x + 2x)(x + 6)

b)

(12x + 2)(x + 2)

c)

14x + 6

d)

(12x + 1)(x + 2)

129.

Select the two numbers that add to - 4 and multiply to -32.

a)

-8

b)

-1

c)

-3

d)

4

130.

Select the two numbers that add to 5 and multiply to 4.

a)

1

b)

4

c)

2

d)

3

131.

Factor by GCF:
63x⁴ - 7x² + 28x

a)

7x(9x² - 7 + 4x)

b)

x(63x³ - 7x + 28)

c)

7x(9x³ - x + 4)

d)

not factorable

132.

Factor by grouping

x³ - 4x² -4x + 16

a)

(x+4)(x+2)

b)

(x-4)(x² -4)

c)

(x+4)(x² -4)

d)

(x-4)(x-2)

133.

Factor by grouping:
4p³+8p²+3p+6

a)

(2p²+3)(p+2)

b)

(2p²+6)(p+4)

c)

(4p²+3)(p+2)

d)

(4p²+8p)(3p+6)

134.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

135.

Find the values of the zeros of the function y=(x+2)(x-3)(3x-5)

a)

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

b)

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

c)

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

d)

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

136.

What is the degree of the function graphed?

a)

2

b)

4

c)

6

d)

8

137.

What is the leading coefficient of the function:

f(x) = 6x² + 4 - 3x⁴ + 5x - 9x³

a)

6

b)

3

c)

-3

d)

4

138.

Simplify:

(4x³ + 2x² - 5x - 9) - (-3x³ - 5x² - x + 11)

a)

7x³ + 7x² - 4x - 20

b)

7x³ - 3x² - 6x + 2

c)

x³ - 3x² - 6x + 2

d)

x³ + 7x² - 4x - 20

139.

Match the following End Behavior to their Graphs

a)

1.

Degree is Odd, Leading Coefficient is Negative

b)

2.

Degree is Odd, Leading Coefficient is Positive

c)

3.

Degree is Even, Leading Coefficient is Negative

d)

4.

Degree is Even, Leading Coefficient is Positive

140.

Match the following

a)

$-10x$

1.

linear monomial

b)

$9x^5+4x^4+3$

2.

quintic trinomial

c)

$4x-10x^2-2x^4$

3.

quartic trinomial

d)

$9x-4$

4.

linear binomial

e)

$3x-2x^4+10-2x^2$

5.

quartic polynomial

141.

Factor by using GCF: (5 points)

8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

142.

Key Idea

(a) - Product Property

Algebra: If a and b are (b) and (c) , then (d) or (e) .

Choose from the below words

Zero

real numbers

ab = 0

a = 0

b=0

143.

What is the first step in solving (x + 2)(x - 3) = 0 ? (3 points)

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

144.

What are two solutions to the polynomial:
x²+14x=0

a)

x=0, x= 14

b)

x=-14

c)

x= 1, x =10

d)

x= -14, x = 0

145.

Solve: 14m²-12m = 0

a)

m=2 and m=76

b)

m=2 and m=0

c)

m=14 and m=12

d)

m=0 and m=6/7

146.

Factor by using GCF: (5 points)

8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

147.

Key Idea

(a) - Product Property

Algebra: If a and b are (b) and (c) , then (d) or (e) .

Choose from the below words

Zero

real numbers

ab = 0

a = 0

b=0

148.

What is the first step in solving (x + 2)(x - 3) = 0 ? (3 points)

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

149.

What are two solutions to the polynomial:
x²+14x=0

a)

x=0, x= 14

b)

x=-14

c)

x= 1, x =10

d)

x= -14, x = 0

150.

Solve: 14m²-12m = 0

a)

m=2 and m=76

b)

m=2 and m=0

c)

m=14 and m=12

d)

m=0 and m=6/7

151.

Find all roots:
$x^3+4x^2-4x-16=0$

a)

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

b)

{ $-4,\ \pm2$ }

c)

{ $-4,\ 2,\ -3$ }

d)

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

152.

Solve:

x² = 49

a)

± 7

b)

-7

c)

± 2401

d)

7

153.

a)

A

b)

B

c)

C

d)

D

154.

Factor by grouping:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

155.

Solve the trinomial:

12x²-12x - 24 = 0

a)

-1,2

b)

1,2

c)

1,-2

d)

-1,-2

156.

Find all the real zeros of the function
f(x) = 2x³ - 19x² + 38x + 24 given that x-4 is a factor.

a)

x = 1/2, -6

b)

x = -1/2, 6

c)

x = 4, -1/2, 6

d)

x = -4, 1/2, -6

157.

x⁴ - 4x² - 45

a)

(x² - 5)(x - 3)(x + 3)

b)

(x² + 45)(x + 1)(x - 1)

c)

(x² + 5)(x - 3)(x + 3)

d)

(x² + 3)(x - 5)(x + 3)

158.

x⁴ - 48x² - 49

a)

(x² - 7)(x - 7)(x + 1)

b)

(x²+ 49)(x² + 1)

c)

(x - 7)(x - 7)(x² + 1)

d)

(x + 7)(x - 7)(x² + 1)

159.

Factor completely.

x^2+8x-9

a)

$\left(x+3\right)\left(x-3\right)$

b)

$\left(2x+3\right)\left(x-3\right)$

c)

$\left(x-9\right)\left(x+1\right)$

d)

$\left(x-1\right)\left(x+9\right)$

160.

Factor completely.

2x^2-3x-14

a)

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

b)

$\left(2x+2\right)\left(x-7\right)$

c)

$\left(2x-7\right)\left(x+2\right)$

d)

$\left(x-14\right)\left(x+1\right)$

161.

Factor Completely

x^2-49

a)

$\left(x+7\right)\left(x-7\right)$

b)

$7\left(x-7\right)$

c)

$\left(x-7\right)\left(x-7\right)$

d)

$x\left(x-7\right)$

162.

a)

x⁴(x² - 5x - 24)

b)

(x - 8)(x + 3)

c)

x⁴(x - 8)(x + 3)

d)

(x³ - 8)(x³ +3)

163.

How many zeros does the polynomial function
P(x) = 3x⁴+4x-8 have?

a)

1

b)

2

c)

3

d)

4

164.

Solve the following equation. x⁴+4x³ + 3x²= 0

a)

x = 0, x = 3, x = 1

b)

x = -3, x = -1

c)

x = 3, x = 1

d)

x = 0, x = -3, x = -1

165.

Factor Completely:

k⁴ - 10k² - 39

a)

(k² - 13)(k² + 3)

b)

(k - 13)(k + 3)

c)

(k² + 15)(k² - 3)

d)

(k + 13)(k - 3)

166.

Match the following

a)

Dividend

1.

The number being divided in a division problem

b)

Divisor

2.

The number used to divide with in a division problem

c)

Quotient

3.

The answer to a division problem.

d)

Whole Number

4.

The numbers 0,1,2,3,etc...

e)

Mixed Number

5.

$2\ \frac{2}{3}$

167.

What step should you take to begin this problem.

a)

Divide 23x by x and write "23" above 23x.

b)

Divide $4x^2$ by x and write 4x above 23x.

c)

Divide $4x^2$ and 23x by x and then write your answer in order above the dividend.

d)

Multiply -16 by x and 5 and subtract your answer from the dividend.

168.

After dividing $4x^2$ by x and writing 4x above 23x, what is the next step that you should take in solving this problem?

a)

Divide 23x by x and write 23 above -16.

b)

Multiply 4x by x and write $4x^2$ beneath $4x^2$ .

c)

Multiply 4x by x and 5, then write $4x^2+20$ beneath $4x^2+23x$ .

d)

Multiply 4x by x and 5, then write $4x^2+20$ beneath $4x^2+23$ .

169.

The next step you should take is to "subtract." What difference will you find?

a)

$0x^2+3x$

b)

$8x^2+43x$

c)

$8x^2+3x$

d)

$0x^2-3x$

170.

Which selection is the final answer?

a)

$4x+3-31$

b)

$4x-28$

c)

$4x+3-\frac{31}{4x+3}$

d)

$4x+3-\frac{31}{x+5}$

171.

Consider the given polynomial $x^2+3$ . Does the polynomial require placeholders before long division can be performed? If yes, pick the correct placeholder.

a)

No

b)

Yes, 0x should be included.

c)

Yes, $0x^3$ should be included.

d)

Yes, $0x^2$ should be included.

172.

Perform the given division problem. What is your final answer? Take your time, and show your work. This will be graded.

a)

$x+1+\frac{4}{x-1}$

b)

$x-1-\frac{4}{x-1}$

c)

$x+1-\frac{4}{x+1}$

d)

$x+1+\frac{3}{x-1}$

173.

5 is the (a) of the problem.

Choose from the below words

Quotient

Remainder

Divisor

Factor

174.

The answer to a division problem

a)

Divisor

b)

Dividend

c)

Quotient

d)

Remainder

175.

Click on the DIVISOR

A

B

C

D

176.

Click on the DIVIDEND

A

B

C

D

177.

Click on the REMAINDER

A

B

C

D

178.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

179.

a)

2x² + 3x + 8 + -57/x-4

b)

2x² - 13x - 56

c)

2x² + 3x + 8 +7/x-4

d)

2x² - 3x - 16 + -89/x-4

180.

Which term must be inserted in the dividend before you begin long division?

$\left(2x^3+5x^2+9\right)\div\left(x+3\right)$

a)

$0x^4$

b)

$0x^3$

c)

$0x^2$

d)

$0x$

181.

a)

4x - 2

b)

4x + 2

c)

4x - 2 + (1/3x - 1)

d)

4x + 2 + (1/3x - 1)

182.

What is the next step in long division?

Put something up top, Multiply by the outside terms,

a)

Bring the next thing down

b)

Add the terms

c)

Start Over

d)

Subtract the terms

183.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

184.

a)

2x² + 3x + 8 + -57/x-4

b)

2x² - 13x - 56

c)

2x² + 3x + 8 +7/x-4

d)

2x² - 3x - 16 + -89/x-4

185.

Divide
(4b² + b - 2) ÷ (4b + 5)

a)

b + 1 - 3/4b +5

b)

b - 1 + 3/4b - 5

c)

b + 1 + 3/4b + 5

d)

b - 1 + 3/4b + 5

186.

$18\div3=$

(a)

187.

Use polynomial LONG DIVISION to evaluate.

Fill in the blanks!

$\left(21x^3-10x^2-39x+20\right)\div\left(3x-4\right)$

(a) (b) (c) (d) (e)

Choose from the below words

$+6x$

$-5$

$28x^2$

$-39x$

$-15x$

$8x^2$

$+39x$

$15x$

$6$

$+5$

188.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

189.

$\left(2x^5+5x^4-14x^3+17x^2-7x-3\right)\div\left(x-1\right)$ Is x-1 a factor of the polynomial?

a)

Yas

b)

No

190.

-2x²+4x+48 ÷ x+4

a)

-2x+12

b)

2x+12

c)

-4x+9

d)

4x+9

191.

Use synthetic division:
(2x³ - 5x - 7) ÷ (x - 2)

a)

2x³ - 4x² + 3x - 13

b)

2x³ + 4x² +3x - 1

c)

2x² - 4x + 3 - 13/x-2

d)

2x² + 4x + 3 - 1/x-2

192.

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

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

193.

If you are missing an exponent in your polynomial you must put a zero as a coefficient place holder for that exponent

a)

True

b)

False

194.

Use synthetic division

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

195.

Divide using synthetic division $(2x^3+4x^2-5)\div(x+3)$

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

196.

What should be the order of the polynomial ?

(Remember the polynomial must be in order by highest degree)

$\frac{3x-4x^3+6x^4+1}{x+3}$

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

197.

What does it mean to be a factor of a number?

a)

Divides evenly with a remainder of zero.

b)

Divides unevenly with a remainder of 1.

198.

Put the Long Division steps in order

a)

DIVIDE

÷

b)

MULTIPLY

×

c)

SUBTRACT

–

d)

BRING IT DOWN

↓

e)

REPEAT

↖

1)

2)

3)

4)

5)

199.

Perform synthetic division to divide $x^3 - 6x^2 + 11x - 6$ by $x - 2$ .

9th - 11th Final Exam

Total questions: 199

Worksheet time: 3hrs 10mins

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