Free Printable Polynomial Functions

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 number of turns the graph of f(x) could make.

a)

3

b)

2

c)

1

d)

0

3.

f(x) = -3x⁴ + x³ - 2x² + x - 1

What is the degree of f(x)?

a)

3

b)

1

c)

4

d)

2

4.

f(x) = -3x⁴ + x³ - 2x² + x - 1

State the maximum number of turns the graph of f(x) could make.

a)

3

b)

4

c)

2

d)

1

5.

a)

A

b)

B

c)

C

d)

D

6.

a)

A

b)

B

c)

C

d)

D

7.

f(x) = x³ - 3x² - 4x

Find the zeros of f(x).

a)

{-4, 0, 1}

b)

{-1, 4}

c)

{-1, 0, 4}

d)

{-4, 1}

8.

f(x) = 2x³ - x² -x

Find the zeros of f(x).

a)

{-½, 1}

b)

{-1, 0, ½}

c)

{-1, 0, 2}

d)

{-½, 0, 1}

9.

f(x) = x³ - x² - x + 1

Find the zeros of f(x).

a)

{-1, 0, 1}

b)

{-1, 1}

c)

{1}

d)

{-1}

10.

f(x) = x⁴ - 7x³ + 10x²

Find the zeros of f(x).

a)

{0, 2, 5}

b)

{0, 5}

c)

{-4, 0, 2}

d)

{0, 5/3, 2}

11.

Write a polynomial function with the given zeros.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

a)

A

b)

B

c)

C

d)

D

14.

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

a)

3

b)

4

c)

5

d)

0

15.

a)

2

b)

1

c)

4

d)

None

16.

a)

None

b)

1

c)

2

d)

4

17.

Write a polynomial function of least degree with zeros 3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

18.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

19.

Does this function have an absolute maximum?

a)

Yes

b)

No

20.

What is the degree of the polynomial function below?
y = x³ + 4x - 5

a)

3

b)

4

c)

5

d)

98.6

21.

What is the degree of the following function?
y = 25 - x²

a)

25

b)

1

c)

2

d)

-1

22.

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

23.

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

24.

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

25.

Find all zeros for the polynomial function P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

26.

What is the degree of the polynomial function
P(x)=3x⁴-7x²-2x⁷-x+4

a)

4

b)

7

c)

2

d)

11

27.

A polynomial function with rational coefficients of degree 4 MUST have at least 1 rational zero.

a)

True

b)

False

28.

A polynomial function with rational coefficients of degree 3 MUST have at least 1 rational zero.

a)

True

b)

False

29.

A function with degree 3 is called

a)

constant

b)

cubic

c)

linear

d)

quadratic

30.

If f(x) = 4x³ + 5x² - 3, find f(-2).

a)

-415

b)

-15

c)

-55

d)

-615

31.

Simplify:

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

a)

7x³ + 7x² - 6x + 2

b)

x³ - 3x² - 6x + 2

c)

7x³ - 3x² - 6x + 2

d)

x³ + 7x² - 4x + 2

32.

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

33.

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

a)

4x² - 12x + 9

b)

4x² + 12x - 9

c)

4x² - 9

d)

4x² + 9

34.

Which of the following best describes the function?

a)

Monomial

b)

Binomial

c)

Polynomial

d)

Supernomial

35.

Which of the following best describes the function?

a)

Monomial

b)

Binomial

c)

Polynomial

d)

Supernomial

36.

Which of the following best describes the function?

a)

Monomial

b)

Binomial

c)

Polynomial

d)

Supernomial

37.

Which of the following best describes the function?

a)

Monomial

b)

Binomial

c)

Polynomial

d)

Supernomial

38.

Simplify $\left(x-4\right)^3.$

a)

$x^3+12x^2+48x-64$

b)

$64-48x+12x^2-x^3$

c)

$x^3+12x^2-16x-4$

d)

$x^3-12x^2+48x-64$

39.

Find the solution(s) to the equation $y=x^4-16.$ Select all that apply.

a)

$x=-2$

b)

$x=2$

c)

$x=i$

d)

$x=2i$

e)

$x=-2i$

40.

What are the solutions to the equation $f\left(x\right)=x^3-125?$

a)

$x=5,\ -5,\ \frac{5i}{2}$

b)

$x=5,\ \frac{-5+5i\sqrt{3}}{2},\ \frac{-5-5i\sqrt{3}}{2}$

c)

$x=5,\ \frac{-5+\sqrt{75}}{2},\ \frac{-5-\sqrt{75}}{2}$

d)

$x=5,\ 25i,\ -25i$

41.

Find all zeros for the polynomial function
Factor by grouping and then set = 0 to find zeros.
P(x) = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

42.

True or False: If (7x + 4) is a factor of some polynomial function f, then 4/7 is a zero of the function.

a)

True

b)

False

43.

If p(x) = 3x³ - 2x² +6x - 4, find p(-4).

a)

-252

b)

-140

c)

132

d)

180

44.

(x² - 4x + 7) ÷ (x - 2)

a)

x - 6 + (19 / x - 2)

b)

x + 8 - (9 / x - 2)

c)

x - 2 + (11 / x - 2)

d)

x - 2 + (3 / x - 2)

45.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

46.

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

47.

Factor
27x³-64

a)

(3x-4)(9x²+12x+16)

b)

(3x-4)(9x²-12x+16)

c)

(3x+4)(9x²-12x+16)

d)

(3x+4)(9x²+12x+16)

48.

Factor:
x³-12x²+47x-60=0 when 5 is a root.

a)

(x-3)(x-4)(x-5)=0

b)

(x+1)(x-4)(x-5)=0

c)

(x-3)(x-4)(2x-5)=0

d)

(x-5)(x-4)(x-5)=0

49.

Give the correct name for
-3x⁴-3x²+5

a)

Constant Trinomial

b)

Quartic Trinomial

c)

quadratic Trinomial

d)

Linear Trinomial

50.

Give the correct name for
2x³

a)

Quadratic Monomial

b)

Quadratic Trinomial

c)

Linear Monomial

d)

Cubic Monomial

51.

Factor Completely: 4x² - 20x + 25

a)

(4x - 25) (x -1)

b)

(2x + 5) (2x - 5)

c)

(2x - 5)²

d)

(4x - 5) (x - 5)

52.

Factor by grouping:
20x² - 16x - 25x +20

a)

(20x - 5)(x - 4)

b)

(4x + 5)(5x + 4)

c)

(5x - 4)(4x - 5)

d)

(5x + 4)(4x - 5)

53.

Factor completely:
x³+7x²-2x-14

a)

(x²-2)(x-7)

b)

(x²+2)(x-7)

c)

(x²+2)(x+7)

d)

(x²-2)(x+7)

54.

Factor Completely:

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)

55.

Factor: 8x³ - 1

a)

(2x - 1)(4x² + 2x + 1)

b)

(2x + 1)(4x² - 2x + 1)

c)

(2x - 1)(4x² - 2x - 1)

d)

(2x + 1)(4x² +2x + 1)

56.

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)

Polynomial Functions

Total questions: 56

Worksheet time: 3hrs 48mins

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