Free Printable Test 8 Review: Polynomial Functions (B) (22-23)

1.

f(x) = 2x³ - 3x² + 4x -10

What is the degree of f(x)?

a)

3

b)

2

c)

1

d)

0

2.

f(x) = 2x³ - 3x² + 4x -10

State the maximum and minimum number of zeros for f(x).

a)

Max: 3 Min: 0

b)

Max 2 Min: 0

c)

Max: 1 Min: 1

d)

Max: 3 Min: 1

3.

f(x) = -3x⁴ + x³ - 2x² + x - 1

What is the y-intercept of f(x)?

a)

(-1, 0)

b)

(0, -1)

c)

(-3, 0)

d)

(0, -3)

4.

a)

A

b)

B

c)

C

d)

D

5.

f(x) = x³ - x² - x + 1

Find the zeros of f(x).

a)

{-1, 0, 1}

b)

{-1, 1}

c)

{1}

d)

{-1}

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

A

b)

B

c)

C

d)

D

8.

Function: y = -3x⁴ +2x² - 8x + 9.
As x approaches infinity, what does y approach?

a)

infinity

b)

negative infinity

c)

0

d)

-3

9.

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

10.

Select all the even degree functions.

a)

A

b)

B

c)

C

d)

D

11.

Which functions readily show the y-intercept of their graphs?

a)

y = 3x²- 2

b)

y = 5 - 2x + 3x²+ 6x³

c)

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

d)

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

12.

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

a)

Left side: Rises
Right side: Rises

b)

Left Side: Rises
Right side: Falls

c)

Left side: Falls
Right side: Rises

d)

Left side: Falls
Right side: Falls

13.

What are the x-intercepts of the following function?
y = 2(x - 1)(x +3)(x - 4)

a)

1, 3 and 4

b)

2, 1, -3, and 4

c)

-1, 3, and -4

d)

1, -3, and 4

14.

Which standard form function matches the factored form:
y = (x + 1)(x - 3)

a)

y = x² + x - 3

b)

y = x - 2

c)

y = x² - 2x - 2

d)

y = x² - 2x - 3

15.

Which standard form function matches the factored form:
y = (x + 1)(x - 1)(x + 4)

a)

y = x³ - x² - 4x

b)

y = x³ + 4x² - x - 4

c)

y = x³ - 4x² + x + 4

d)

y = x³ + x² - x - 4

16.

How many roots or zeros does the equation
f(x) = 5x⁴-8x³+4x²-6x+3 have?

a)

3

b)

4

c)

5

d)

0

17.

Classify the function:

a)

quadratic

b)

cubic

c)

quartic

d)

linear

18.

What is the leading coefficient of the function:

f(x) = 6x² + 4 - 3x⁴ + 5x - 9x³

a)

6

b)

3

c)

-3

d)

4

19.

Which of the following is a 5th degree trinomial with a leading coefficient of -2?

a)

-2x⁵ + 3x - 1

b)

5x^-2 +3x - 1

c)

-2x⁵ + 3x⁴ + 2x³ + x² - 10

d)

2x + 5

20.

Choose the best equation to match the graph.

a)

$y=\left(x-2\right)\left(x-4\right)\left(x-8\right)$

b)

$y=-\left(x-2\right)\left(x-4\right)\left(x-8\right)$

c)

$y=\left(x+2\right)\left(x+4\right)\left(x+8\right)$

d)

$y=-\left(x+2\right)\left(x+4\right)\left(x+8\right)$

21.

Which of the following could NOT represent the function above?

a)

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

b)

$y=\left(x+3\right)\left(x^2+4\right)$

c)

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

d)

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

22.

What are the "zeros" of this polynomial?

a)

-2, -1

b)

-2, -1, 0, 1, 2

c)

-2, -1, 1, 2

d)

-2, -1, 4, 1, 2

23.

Identify a possible equation.

a)

$g\left(x\right)=\left(x+3\right)\left(x+1\right)\left(x+5\right)$

b)

$g\left(x\right)=\left(x-3\right)\left(x-1\right)\left(x-5\right)$

c)

$g\left(x\right)=\left(x-3\right)\left(x-1\right)\left(x+5\right)$

d)

$g\left(x\right)=\left(x+3\right)\left(x+1\right)\left(x-5\right)$

24.

What is the degree of the above polynomial graph?

a)

3

b)

4

c)

5

d)

6

25.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

26.

What is the leading coefficient?

a)

Positive

b)

Negative

c)

Odd

d)

Even

27.

The function shown has:

a)

Degree two with negative leading coefficient.

b)

Degree three with negative leading coefficient.

c)

Degree four with negative leading coefficient.

d)

Degree four with positive leading coefficient.

28.

Which description best matches the function shown:

a)

Odd degree with positive leading coefficient.

b)

Even degree with positive leading coefficient.

c)

Degree three, with negative leading coefficient.

d)

Degree four, with negative leading coefficient.

29.

The polynomial
f(x) = 5x⁴ + 2x³ + 2x − 7 can have, at most, how many solutions?

a)

5

b)

4

c)

3

d)

2

30.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

31.

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

32.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

33.

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.

34.

How many zeros (real and imaginary) would the polynomial have?
f(x) = 5x - 2x² + 8x⁵ - 8

a)

1

b)

2

c)

4

d)

5

35.

A term that only contains a number.

a)

term

b)

polynomial

c)

coefficient

d)

constant

36.

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

a)

Yes

b)

No

37.

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!

38.

Find all the factors of x³ -3x² -4x +12 given that -2 is a zero.

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)

39.

Find all the zeros, given that f(-3) = 0

f(x) = 2x³+5x²-6x-9

a)

-1,-3,-3

b)

-2,-3,3

c)

3,3,3

d)

-3,2/3,-1

40.

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

a)

-2

b)

-6

c)

-12

d)

0

41.

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)

42.

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

a)

-25

b)

25

c)

113

d)

-113

43.

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

44.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙+𝟐, then what is the remainder?

a)

0

b)

-3

c)

9

d)

5

45.

According to this work, is x-3 a factor of $p\left(x\right)=5x^3-2x^2+x-120$ ?

a)

Yes, x-3 is a factor of p(x) since the remainder is 0.

b)

No, x-3 is not a factor of p(x) since the remainder is 0.

46.

This work shows $x^2-3x+5\div x-2$ . What information does this reveal?

a)

x-2 is not a factor of $x^2-3x+5$ since the remainder is 3.

b)

x-2 is a factor of $x^2-3x+5$ since the remainder is 3.

47.

This work shows $x^2-3x+5\div x-2$ . What information does this reveal?

a)

2 is a solution of $x^2-3x+5$ since the remainder is 3.

b)

2 is not a solution of $x^2-3x+5$ since the remainder is 3.

48.

Match the following appropriately.

It is important you can recognize the connection between factors and solutions.

a)

1 is a solution of p(x).

1.

2x - 3 is a factor of p(x).

b)

3 is a solution of p(x).

2.

x-1 is a factor of p(x).

c)

3/2 is a solution of p(x).

3.

x - 3 is a factor of p(x).

d)

0 is a solution of p(x).

4.

x is a factor of p(x).

49.

Match the following appropriately.

It is important you can recognize the connection between factors and solutions.

a)

x + 3 is a factor of p(x).

1.

-3 is a solution of p(x).

b)

x - 5 is a factor of p(x).

2.

5 is a solution of p(x).

c)

3x - 5 is a factor of p(x).

3.

5/3 is a solution of p(x).

d)

x + 5 is a factor of p(x).

4.

-5 is a solution of p(x).

50.

What do we know about p(x)= $3x^4+2x^3-5x+4$ based off of the work shown here?

Read carefully

a)

1 is a solution

b)

1 is not a solution

c)

x -1 is a factor

d)

x+1 is not a factor

51.

Match the following:

a)

is a factor of $5x^2-10x-40$

1.

x + 2...

b)

is a solution of $5x^2-10x-40$

2.

-2...

c)

0

3.

The remainder is...

d)

x+2

4.

5x² -10x - 40 is being divided by...

52.

This work shows $x^3+2x^2-58x-35\div x-7$ . What does this reveal?

More than one answer is correct.

a)

x-7 is a factor of p(x).

b)

x+7 is a factor of p(x).

c)

-7 is a solution of p(x).

d)

7 is a solution of p(x).

53.

Which statement accurately describes what this work demonstrates?

a)

x+6 is a factor of $x^3-x^2-40x\ +13$ .

b)

x+6 is not a factor of $x^3-x^2-40x\ +13$ .

c)

x-6 is not a factor of $x^3-x^2-40x\ +13$ .

d)

x-6 is a factor of $x^3-x^2-40x\ +13$ .

54.

Complete the problem shown here.

Use the remainder to determine whether 5 is a solution of $p\left(x\right)=2x^3-12x^2+11x-5$ .

a)

5 is a solution of p(x) since the remainder is 0.

b)

5 is a solution of p(x) since the remainder is 100.

c)

5 is not a solution of p(x) since the remainder is 0.

d)

5 is not a solution of p(x) since the remainder is 100.

55.

Complete the problem shown here.

Use the remainder to determine whether x-5 is a solution of $p\left(x\right)=2x^3-12x^2+11x-5$ .

a)

x-5 is a factor of p(x) since 5 was a solution.

b)

x-5 is not a factor of p(x) since 5 was not a solution.

c)

x+5 is not a factor of p(x) since 5 was not a solution.

d)

x+5 is a factor of p(x) since 5 was a solution.

56.

The work here shows that dividing $x^2+16$ by x+4 results in a remainder of 32. Which statement is true based upon that work shown here?

a)

-4 is a solution of $x^2+16$

b)

4 is a solution of $x^2+16$

c)

x+4 is not a factor of $x^2+16$

d)

x-4 is not a factor of $x^2+16$

57.

This work shows $4x^2+17\div x+2$ .

a)

True

b)

False

58.

Complete the synthetic division and use the remainder to determine a true statement concerning p(x) and its solutions.

a)

-2 is a solution of p(x) since the remainder is equal to 0.

b)

-2 is not a solution of p(x) since the remainder is equal to 1.

c)

-2 is not a solution of p(x) since the remainder is equal to 33.

d)

2 is not a solution of p(x) since the remainder is equal to -1.

59.

Complete the rest of this synthetic division problem.

Determine the remainder.

a)

The remainder is 18.

b)

The remainder is 0.

c)

The remainder is 108.

d)

The remainder is 28.

60.

Based on the remainder you found, which statement is true?

a)

3 is a solution of $2x^3-15x+9$ .

b)

3 is not a solution of $2x^3-15x+9$ .

c)

-3 is a solution of $2x^3-15x+9$ .

d)

-3 is not a solution of $2x^3-15x+9$ .

61.

Based on the remainder you found, which statement is true?

a)

x-3 is not a factor of $2x^3-15x+9$ .

b)

x-3 is a factor of $2x^3-15x+9$ .

c)

x+3 is not a factor of $2x^3-15x+9$ .

d)

x+3 is a factor of $2x^3-15x+9$ .

62.

Assume that a polynomial has a solution at the x-value 4.

Which of the following must be a factor of that same polynomial?

a)

4x

b)

x-4

c)

x+4

63.

Assume that x-2 is a factor of a polynomial. Which x-value must be a solution of that same polynomial?

a)

The x-value -2

b)

The x-value 2

c)

The x-value 0

64.

Finish dividing $p\left(x\right)=5x^3+34x^2+26x+C$ by x+6. Determine what value C must equal if x+6 is a factor of p(x).

a)

C would need to be equal to 0.

b)

C would need to be equal to 12.

c)

C would need to be equal to -12.

d)

C would need to be equal to 300.

65.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

66.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

67.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

a)

±1, ±5, ±1/2, ±5/2

b)

±1, ±2, ±5, ±1/2, ±5/2

c)

±1, ±5

d)

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

68.

Solve by using Rational Root Theorem:
2x³ - 11x² + 12x + 9 = 0

a)

-1, 1, 3

b)

-1, 3/2, 3

c)

-1/2, 3, 3

d)

-1/2, 1, 3

69.

Solve by using Rational Root Theorem:
x³ - 7x - 6 = 0

a)

1, 2, 3

b)

-1, -2, - 3

c)

-1, -2, 3

d)

1,-2,-3

70.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

71.

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

a)

-3

b)

-4

c)

1

d)

6

72.

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ - 8x² - 23x + 30

a)

3

b)

-1

c)

-10

d)

1

73.

What are the zeros of the polynomial

g(x) = 2x⁴ -19x³ + 46x² + 7x - 60

a)

-1,4,5,3/2

b)

-1,-4,5,-3/2

c)

1,4,5,3/2

d)

-1,4,5,2/3

74.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

75.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

76.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

77.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

Test 8 Review: Polynomial Functions (B) (22-23)

Total questions: 77

Worksheet time: 5hrs 41mins

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