Free Printable IM3 Unit 3 Polynomial Functions review

1.

What is the degree of the polynomial?

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

a)

4

b)

3

c)

2

d)

1

2.

What is the leading term of the polynomial?

f\left(x\right)\ =\ 3x^3-6x^5-2x^2-5\ ?

a)

$3x^3$

b)

$-6x^5$

c)

$-2x^2$

d)

-5

3.

Check all the even degree polynomials:

a)

b)

c)

d)

e)

4.

What of the following is a correct end behavior?

a)

as\ x\ \longrightarrow\infty,\ f\left(x\right)\longrightarrow\ \infty\

b)

$as\ x\ \longrightarrow\infty,\ f\left(x\right)\longrightarrow-\infty$

5.

What of the following is a correct end behavior?

a)

as\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow\ \infty\

b)

$as\ x\ \longrightarrow-\infty,\ f\left(x\right)\longrightarrow-\infty$

6.

What is the y-intercept of the function graphed?

a)

(0, -4)

b)

(-1, 0)

c)

(0, 4)

d)

(2, 0)

7.

Which of the following is NOT an x-intercept?

a)

(-1, 0)

b)

(2, 0)

c)

(4, 0)

d)

(0, -4)

8.

Match each x-intercept with it's multiplicity.

a)

(-1, 0)

1.

2

b)

(2, 0)

2.

3

c)

(4, 0)

3.

1

d)

(0, -4)

4.

This is not an x-intercept.

9.

What is the end behavior for this function?

a)

as x→∞, y→∞;

as x→-∞, y→∞

b)

as x→∞, y→-∞;

as x→-∞, y→-∞

c)

as x→∞, y→∞;

as x→-∞, y→-∞

d)

as x→∞, y→-∞;

as x→-∞, y→∞

10.

Use synthetic division to determine which of the following is a root of the function $f\left(x\right)=5x^3-31x^2+31x-5$ .

a)

0

b)

1

c)

-1

d)

-5

11.

Is (x-5) a factor of the polynomial x³-4x²+5x-20

a)

Yes

b)

No

12.

Describe the transformations to x³.
f(x)=2(x-4)³

a)

Stretch of 2, and shifts left 4

b)

Stretch of 2 and shifts right 4

c)

Shifts up 2 and left 4

d)

Stretch of 2 and down 4

13.

What is the leading coefficient?

a)

Positive

b)

Negative

14.

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

List the zeros for this function.

a)

x=-4, x=3, x=-2

b)

x=-4, x=3, x=2

c)

x=-4, x=3, x=-2

d)

x=4, x=3, x=2

15.

What is the decreasing interval(s) of the function behind this text?

a)

(-∞,∞)

b)

(-∞, 1)

c)

(-∞, 0)

d)

None

16.

How may real solutions does the function have?

a)

0

b)

1

c)

2

d)

3

17.

Possible factored form of f(x)

a)

$f(x)=(x-2)(x+1)$

b)

$f(x)=(x+2)(x-1)$

c)

$f(x)=(x-2)(x+1)^2$

d)

$f(x)=(x+2)(x-1)^2$

18.

Match the graph to the function

a)

f(x)= -x²+3x+2

b)

f(x) = -x³+2

c)

f(x) = x³+2

d)

f(x) = ⅓x⁴-5x²+2

19.

Name the polynomial by degree and number of terms.

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

a)

Cubic polynomial of 3 terms

b)

Quartic Trinomial

c)

Quadratic Trinomial

d)

Quadratic Polynomial of 4 terms

20.

Divide:

\frac{m^3-m^2-20m-53}{m-6}

a)

$m^2+5m+10$

b)

$m^2+5m+10\ R:\ 7$

c)

$m^2-5m-10\ R:\ 7$

d)

$m^2-7x+22\ R:\ -185$

21.

Choose the correct graph for the following function:

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

a)

b)

c)

d)

22.

Perform the indicated operation . Write the answer in standard form ( 3x² - 8x + 7 ) + ( 8x² + 9x - 16 )

a)

11x⁴ + x² - 9

b)

11x² - x - 9

c)

11x² -17x - 11

d)

11x² + x - 9

23.

The (a) is the greatest power of the variable in a polynomial expression.

24.

A polynomial that contains 3 terms is called a ________________________.

a)

binomial

b)

monomial

c)

trinomial

d)

triomial

25.

Is (x-4) a factor of the polynomial x³-4x²+5x-20

a)

Yes

b)

No

26.

Is (x-5) a factor of the polynomial x³-4x²+5x-20

a)

Yes

b)

No

27.

When setting up this synthetic division, what polynomial is being divided?

a)

2x⁴ + 3x² - x + 2

b)

2x⁴ + 3x³ - x² + 2

c)

2x⁴ - 3x² + x - 2

d)

cannot be determined

28.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

29.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

30.

Find the product:
(m+11)²

a)

m²+22m+121

b)

m²+11m+121

c)

m²+11m +11

d)

m²+22m +11

31.

Find the correct statement about the zeros.

a)

−5 is a zero with multiplicity 1

b)

−5 is a zero with multiplicity 2

c)

−2 is a zero with multiplicity 1

d)

2 is a zero with multiplicity 2

32.

$f\left(x\right)=x^4-3x^3-12x^2+15x-34$ at x=5

a)

-9

b)

8

c)

-1

d)

6

33.

Which point does not represent a zero of a polynomial?

a)

(-2, 0)

b)

(-1, 0)

c)

(0, 4)

d)

(2, 0)

34.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

35.

What is the predicted end behavior of: y=-2x⁴+3x-1

a)

up on both ends

b)

down on both ends

c)

up on left, down on right

d)

down on left, up on right

36.

What are the roots?

$y=5x^2+5x-30$

a)

$\left\{-2,\ 3\right\}$

b)

$\left\{-3,\ 2\right\}$

c)

$\left\{0,-30\right\}$

d)

$\left\{2,\ 0\right\}$

37.

What is another word for zeros?

a)

solutions

b)

x -intercepts

c)

roots

d)

All of the these!

38.

Determine the roots of the polynomial.
f(x) = -x(x+1)(x-3)

a)

-1, 3

b)

0, -1, 3

c)

1, -3

d)

0, -3, 1

39.

Which one of the following functions is even?

a)

f(x) = x⁴ + x³

b)

g(x) = x⁴ + x²

c)

h(x) = x⁵ + x³

d)

k(x) = x³ + x

40.

Which one of the following functions is odd?

a)

f(x) = 3x⁴ - 4x³

b)

g(x) = 5x⁴ + 3x²

c)

h(x) = 6x⁵ - x³

d)

k(x) = x⁶ + 8x²

41.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

42.

$4x^3-3x^2+5x-7$ What is the degree of the polynomial?

a)

2

b)

3

c)

1

d)

0

43.

Select ALL transformations that y= -2x⁸+7 makes to the parent function y=x⁸

a)

flip

b)

wider

c)

thinner

d)

move up

e)

move down

44.

Match the equation to its description.

a)

Vertical Stretched by 2 and translation up 4

b)

Vertical Compressed by 2 and translation up 4

c)

Horizontal Stretched by 2 and translation left 4

d)

Horizontal Compressed by 2 and translation right 4

45.

In the equation f(x)=1/2(x+9)²-1, what happens to the parabola?

a)

Reflect, horizontal compress by 1/2, left 9, down 1

b)

Vertical compress by 1/2, left 9, down 1

c)

Horizontal Compress by 1/2, right 9, down 1

d)

Vertical Stretch by 1/2, left 9, down 1

46.

Describe the transformation of the graph y = -2(x + 5)³

a)

Shrink by 2, Reflected over y-axis, Right 5

b)

Stretch by 2, Reflected over x-axis, Left 5

c)

Stretch by 2, Reflected over x-axis, Right 5

d)

Shrink by 2, reflected over y-axis, Left 5

47.

The function is translated (a) units to the right and four units (b) . Then it is (c) across the line (d) .

Choose from the below words

two

up

reflected

y=4

48.

Which expression shows the factors of: n² + 16n + 63?

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

49.

Which expression is equivalent to

the polynomial: k²+7x+10?

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

50.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

51.

Solve using Zero-Product Property
(x - 11)(5x + 1) = 0

a)

x = 11 or x = -1/5

b)

x = -11 or x = -1/5

c)

x = 11 or x = 1/5

d)

x = -11 or x = 1/5

52.

What are the solutions for

$\left(x-5\right)\left(x+2\right)=0$

a)

$x=-5$ $x=2$

b)

$x=5$ $x=-2$

c)

$x=3$

d)

$x=0$

53.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

54.

What is the lead coefficient of the polynomial?

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

55.

Choose all the binomial expressions.

a)

-5x + 12

b)

2x²

c)

2y²- 2y + 2

d)

19 - 7y

e)

3x³ - 3

56.

Combine like terms (to put the polynomial in standard form).

a)

2x² + 6x

b)

x² + 8x

c)

2x⁴ + 6x

d)

3x² + 6x

57.

What is the leading coefficient of this polynomial? REMEMBER: The polynomial must be in STANDARD FORM.

a)

1

b)

2

c)

3

d)

6

58.

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

a)

- 3x³ - x² - 10x + 12

b)

3x³ - x² + 10x + 12

c)

12 - 3x³ - 10x - x²It is in Standard Form.

d)

12 - 10x - 3x³ - x²

59.

What is the end behavior of this function?

a)

As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \

As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty

b)

$As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

c)

$\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$

d)

$As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

60.

What is the end behavior of this function?

a)

As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty\ \ \

As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty

b)

$As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow\infty\$ $\ \ \ As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow-\infty$

c)

$\ As\ x\longrightarrow\ -\infty,\ f\left(x\right)\longrightarrow-\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty\$

d)

$As\ x\longrightarrow-\ \infty,\ f\left(x\right)\longrightarrow\infty$ $As\ x\longrightarrow\ \infty,\ f\left(x\right)\longrightarrow\infty$

61.

Which one means left

a)

x →-∞

b)

x →∞

62.

Complete the end behavior statement using the degree and leading coefficient: $f\left(x\right)=-x^7+2x^2+3x-4$ .

As

x\rightarrow\infty,\ y\rightarrow\ ?

a)

$\infty$

b)

$-\infty$

63.

Complete the end behavior statement using the degree and leading coefficient: $f\left(x\right)=3x^6+2x^3-12x+1$ .

As

x\rightarrow-\infty,\ y\rightarrow\ ?

a)

$\infty$

b)

$-\infty$

64.

Which equation could be graphed here?

a)

f(x) = - x⁴+ 2x +9

b)

f(x) = 2x³ + 2x²+ 10

c)

f(x) = -4x⁵ - x⁴ + 3x² + 11

d)

f(x) = 6x⁴ +3x³ - 2x + 14

65.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

66.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 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

67.

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

a)

0

b)

1

c)

2

d)

3

68.

Find the remainder using the Remainder Theorem:

(x²- 6x + 8) ÷ (x - 2)

a)

1

b)

2

c)

0

d)

3

69.

Use the Complex Conjugate Root Theorem to state another complex solution. Given that 3+5i is a root.

a)

-3+5i

b)

-3-5i

c)

-5i

d)

3-5i

70.

Multiply (6 - 2i)(6 + 2i)

a)

40

b)

32

c)

$36-i^2$

d)

36-12i

IM3 Unit 3 Polynomial Functions review

Total questions: 70

Worksheet time: 2hrs 22mins

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