Free Printable Factoring Polynomials Mixed Practice

Worksheets

Factoring Polynomials Mixed Practice

Total questions: 30

Worksheet time: 41mins

Name

Class

Date

Which expression below represents a polynomial?

$2x^{-3}+x^2-10$

$\frac{1}{x}-5$

$x^{0.5}+6x-3$

$x^2-3x+7$

The degree of the polynomial given by

y = 3x² + 9x⁵ − 4 + 10x⁸ + 2x⁹ is:

-4

What is the degree of this polynomial?

2x⁴- 3x⁵+ x

-3

Which of the following polynomials is written in standard form?

y = 7x³ − 5x² + 2x + 7

y = 8 − 4x² + 3x + 2x³

y = 10x² − 5x⁵+ 2x + 20

y = 1 + 2x² − 3x³ + 4x⁴

How many terms are in this polynomial?

2x³- 8x²+ 3x - 7

What is the first step when factoring polynomials?

Find the GCF

List all the terms

Make a triangle

Write the answer

What is the GCF?
$28p^3+16p^2+16p$

$2p$

$4p$

$4p^2$

$8p^{2\ }$

Which binomials are a difference of two squares?

I. 6a²-25

II. 4x²+16

III. b²-9

IV. 49y²-64

I only

III only

III and IV

II, III, and IV

Factor p³- 3p² - 16p + 48

p² ( p - 3) (p - 3)

(p² - 16) (p - 3)

(p + 4) (p - 4) (p - 3)

10.

Factor: x²+9x+18

(x+6)(x+3)

(x-6)(x-3)

(x-6)(x+3)

(x+6)(x-3)

11.

What is the factored form of x³+7x²-2x-14

(x²-2)(x-7)

(x²+2)(x-7)

(x²+2)(x+7)

(x²-2)(x+7)

12.

Fully Factor the Following

25x²-81

(5x-9)²

(5x+9)(5x-9)

25(x-9)²

(9x+5)(9x-5)

13.

Factor

81m² - 1

not factorable

(m-9)(m+9)

9m(9m-1)

(9m-1)(9m+1)

14.

Factor: 3x²-17x+10

(x-5)(3x-2)

(x+5)(3x+2)

(3x-5)(x-2)

(x+5)(3x-2)

15.

Factor: 4x²-16x-9

(2x-9)(2x+1)

(2x+9)(2x-1)

(4x-1)(x+9)

(x+1)(4x-9)

16.

Factor: x³ + 11x² + 10x

(x+1) (x+10)

x(x+1) (x+10)

(x²+1) (x+10)

PRIME

17.

Factor Completely:

3x⁴ + 3x³ - 12x² - 12x

3x(x³ + x²- 4x - 4)

3x(x²-4)(x+1)

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

3x(x²+4)(x-1)

18.

Factor: 27x³ + 8

(3x + 2)(9x² - 6x + 4)

(9x + 2)(3x² + 18x + 4)

(3x²+4)(9x + 2)

(27x + 8)(x² - 216x + 64)

19.

Factor Completely:

k⁴ - 10k² - 39

(k² - 13)(k² + 3)

(k - 13)(k + 3)

(k² + 15)(k² - 3)

(k + 13)(k - 3)

20.

Factor Completely:

4w⁴ + 16w² + 15

(w² + 10)(w² + 6)

(2w²+ 5)(2w² + 3)

(w² + 15)(4w² + 1)

(2w + 5)(2w + 3)

21.

Factor Completely:

14x⁴+x²-3

(7x²+ 3)(2x²- 1)

(7x²- 3)(2x²+ 1)

(14x²- 3)(1x²+ 1)

(7x+ 3)(3x+ 1)

22.

Factor Completely:

256x⁴ - 81

(16x²+ 9)(16x²- 9)

(16x²+ 9)(4x + 3)(4x - 3)

(4x²+ 9)(4x²- 9)

(16x²+ 9)(2x + 6)(2x -6)

23.

x⁶- 400

( x³ - 200) ( x³ + 200)

( x² + 20) ( x² + 20)

( x - 20) ( x + 20)

( x³ - 20) ( x³ + 20)

24.

x⁴ - 100y²

(x² + 10y) (x² - 10y)

(x + 10y) (x - 10y)

(x + 10y) (x³ - 10y)

(x³ + 10y) (x - 10y)

25.

Factor completely.

8x⁶ - 64

Prime

8(x²- 2)³

8(x²-2)(x⁴+2x²+4)

8(x-2)⁶

26.

Factor

k⁴+7x²+10

(k²+2)(k²+5)

(k²-2)(k²-5)

(k+10)(k+4)

(k+2)(k+5)

27.

Factor

2x⁴ - 13x² - 70

(2x+7)(x-10)

(7x+5)(x+2)

(2x²+7)(x²-10)

2(x²+7)(x²+10)

28.

Factor:

17xy² - xy

17(xy² - x)

y(17xy - x)

xy(17y - 1)

prime

29.

Factor completely: -5x²+ 30x - 40

-5(x-2)(x-4)

(x-2)(x-4)

-(5x-8)(x-5)

(5x+10)(x+4)

30.

Factor Completely:

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

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

$\left(x+2\right)\left(x-2\right)\left(x+1\right)$

$\left(x^2+4\right)\left(x+1\right)$

Prime

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Factoring Polynomials Mixed Practice

Total questions: 30

Worksheet time: 41mins

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