Free Printable Polynomial Functions unit test

Worksheets

Polynomial Functions unit test

Total questions: 28

Worksheet time: 1hrs 10mins

Name

Class

Date

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

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

Which function is graphed?

(x - 4)(x + 2)(x - 8)=0

(x - 4)(x - 2)(x + 8)=0

(x - 4)(x + 2)(x + 8)=0

(x + 4)(x + 2)(x + 8)=0

What is the end behavior for
f(x)= -x³+2x+1

Simplify: (5x+2)(x²-3x+6)

5x³- 17x²+24x +12

5x³+ 17x² - 24x +12

5x³ - 13x² + 24x +12

5x³ +13x² - 24x - 12

What is the leading coefficient?

Positive

Negative

Odd

Even

What is the degree?

Positive

Negative

Odd

Even

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

-∞
-∞

+∞
-∞

-∞
+∞

+∞
+∞

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

10.

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

11.

Determine all of the linear factors for the polynomial x³-12x²+47x-60=0 when given that x = 5 is a root.

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

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

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

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

12.

Determine the end behavior of the graph of

f(x) = -3x³ + 2x - x⁴ (Use desmos.com to graph the function.)

As x →∞, f(x) →∞.

As x→-∞, f(x) →-∞.

As x →∞, f(x) →∞.

As x→-∞, f(x) →∞.

As x →∞, f(x) →-∞.

As x→-∞, f(x) →∞.

As x →∞, f(x) →-∞.

As x→-∞, f(x) →-∞.

13.

State the minimum degree of the function shown:

14.

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

Leading Coefficient Positive
Degree - Even

Leading Coefficient Positive
Degree - Odd

Leading Coefficient Negative
Degree - Even

Leading Coefficient Negative
Degree - Odd

15.

Which statement is correct?

The zeros of this polynomial are 0, 2, and 5.

The solution 5 has a multiplicity of 2

The solution 1 has a multiplicity of 1

There are 4 solutions.

16.

Factor or graph the following:

x³ + x²- 16x - 16

Not factorable

(x + 1)(x²+ 16)

(x + 1) (x + 4) (x - 4 )

x² (x + 1) - 32x

17.

Which equation MOST LIKELY matches the graph? (Use your End Behavior Reference Sheet.)

y = x⁴- x³ + 3x² + 2

y = -x⁴ + x³ + 5x + 2

y = x³ - 2x² + 1x + 3

y = -x³ - 2x² + 1x + 3

18.

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

y = x² + x - 3

y = x - 2

y = x² - 2x - 2

y = x² - 2x - 3

19.

The degree of the polynomial determines the number of roots.

True

False

20.

Give the correct name for
2x³

Quadratic Monomial

Quadratic Trinomial

Linear Monomial

Cubic Monomial

21.

Determine the y-intercept
f(x) = x³ - 5x² - 25x + 125

(0,0)

(0,25)

(0,125)

(0,5)

22.

Do synthetic division with x = -2 for
f(x) = x⁴-6x³+7x²+6x-8 and then classify x = -2 properly.

x = -2 is a zero.

x = -2 is an upper bound.

x = -2 is a lower bound.

x = -2 is not a zero or an upper or lower bound.

23.

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

-2

-6

-12

24.

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

-7

25.

Classify by number of terms:
3x³ – 6x

Monomial

Binomial

Trinomial

4-Term Polynomial

26.

Classify by degree of polynomial:
2x – 9

Constant

Linear

Quadratic

Cubic

27.

Determine the dimensions of the cubes below if the length of the smaller cube is one half the length of the larger cube, and the volume of the shaded figure is 23,625 cubic centimeters.

4 lines

28.

Name your mate. Who is this?

4 lines

100 %

Polynomial Functions unit test

Total questions: 28

Worksheet time: 1hrs 10mins

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