Factoring Higher-Degree Polynomials

Question 1

Factor completely: x^4 - 40x^2 + 144.

Accepted Answer

(x - 2)(x + 2)(x - 6)(x + 6)

Answer

(x - 4)(x + 4)(x - 36)(x + 36)

Answer

(x - 12)(x + 12)(x - 1)(x + 1)

Answer

(x - 6)^2(x + 2)^2

Question 2

Factor completely: 2x^4 - 32.

Accepted Answer

2(x - 2)(x + 2)(x^2 + 4)

Answer

2(x - 2)(x + 2)(x^2 - 4)

Answer

2(x - 4)(x + 4)(x^2 + 16)

Answer

2(x - 2)^2(x^2 + 4)

Question 3

Factor completely: 2x^4 - 162.

Accepted Answer

2(x - 3)(x + 3)(x^2 + 9)

Answer

2(x - 3)(x + 3)(x^2 - 9)

Answer

2(x - 9)(x + 9)(x^2 + 81)

Answer

2(x - 3)^2(x^2 + 9)

Question 4

Factor completely: x^4 - 37x^2 + 36.

Accepted Answer

(x - 1)(x + 1)(x - 6)(x + 6)

Answer

(x - 1)(x + 1)(x - 36)(x + 36)

Answer

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

Answer

(x - 6)^2(x + 1)^2

Question 5

Factor completely: x^4 - 29x^2 + 100.

Accepted Answer

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

Answer

(x - 4)(x + 4)(x - 25)(x + 25)

Answer

(x - 10)(x + 10)(x - 1)(x + 1)

Answer

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

Question 6

Factor completely: x^3 + 2x^2 - 16x - 32.

Accepted Answer

(x + 2)(x - 4)(x + 4)

Answer

(x - 2)(x - 4)(x + 4)

Answer

(x + 2)(x - 4)^2

Answer

(x + 2)(x + 4)^2

Question 7

Factor completely: 5x^4 - 5.

Accepted Answer

5(x - 1)(x + 1)(x^2 + 1)

Answer

5(x - 1)(x + 1)(x^2 - 1)

Answer

5(x - 1)^2(x^2 + 1)

Answer

5(x - 1)(x + 1)(x^2 + 2)

Question 8

Factor completely: x^3 + 4x^2 - x - 4.

Accepted Answer

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

Answer

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

Answer

(x + 4)(x - 1)^2

Answer

(x + 4)(x + 1)^2

Question 9

What is the first step in factoring 2x^3 - 12x^2 + 5x - 30?

Accepted Answer

group it as (2x^3 - 12x^2) + (5x - 30)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 2x

Question 10

Factor completely: 3x^4 - 3.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 11

Factor completely: x^4 - 25x^2 + 144.

Accepted Answer

(x - 3)(x + 3)(x - 4)(x + 4)

Answer

(x - 9)(x + 9)(x - 16)(x + 16)

Answer

(x - 12)(x + 12)(x - 1)(x + 1)

Answer

(x - 4)^2(x + 3)^2

Question 12

What is the first step in factoring 2x^3 - 4x^2 + 7x - 14?

Accepted Answer

group it as (2x^3 - 4x^2) + (7x - 14)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 2x

Question 13

Factor completely: x^4 - 52x^2 + 576.

Accepted Answer

(x - 4)(x + 4)(x - 6)(x + 6)

Answer

(x - 16)(x + 16)(x - 36)(x + 36)

Answer

(x - 24)(x + 24)(x - 1)(x + 1)

Answer

(x - 6)^2(x + 4)^2

Question 14

Factor completely: x^3 + 6x^2 - 9x - 54.

Accepted Answer

(x + 6)(x - 3)(x + 3)

Answer

(x - 6)(x - 3)(x + 3)

Answer

(x + 6)(x - 3)^2

Answer

(x + 6)(x + 3)^2

Question 15

Factor completely: 3x^4 - 48.

Accepted Answer

3(x - 2)(x + 2)(x^2 + 4)

Answer

3(x - 2)(x + 2)(x^2 - 4)

Answer

3(x - 4)(x + 4)(x^2 + 16)

Answer

3(x - 2)^2(x^2 + 4)

Question 16

Factor completely: x^4 - 5x^2 + 4.

Accepted Answer

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

Answer

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

Answer

(x - 1)(x + 1)(x^2 + 4)

Answer

(x - 2)^2(x + 1)^2

Question 17

Factor completely: x^3 + 3x^2 - 25x - 75.

Accepted Answer

(x + 3)(x - 5)(x + 5)

Answer

(x - 3)(x - 5)(x + 5)

Answer

(x + 3)(x - 5)^2

Answer

(x + 3)(x + 5)^2

Question 18

Factor completely: x^3 + 5x^2 - 4x - 20.

Accepted Answer

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

Answer

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

Answer

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

Answer

(x + 5)(x + 2)^2

Question 19

What is the first step in factoring 4x^3 - 24x^2 + 5x - 30?

Accepted Answer

group it as (4x^3 - 24x^2) + (5x - 30)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 4x

Question 20

What is the first step in factoring 3x^3 - 12x^2 + 7x - 28?

Accepted Answer

group it as (3x^3 - 12x^2) + (7x - 28)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 3x

Question 21

What is the first step in factoring 5x^3 - 30x^2 + 3x - 18?

Accepted Answer

group it as (5x^3 - 30x^2) + (3x - 18)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 5x

Question 22

Factor completely: x^3 + x^2 - 4x - 4.

Accepted Answer

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

Answer

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

Answer

(x + 1)(x - 2)^2

Answer

(x + 1)(x + 2)^2

Question 23

Factor completely: 6x^4 - 486.

Accepted Answer

6(x - 3)(x + 3)(x^2 + 9)

Answer

6(x - 3)(x + 3)(x^2 - 9)

Answer

6(x - 9)(x + 9)(x^2 + 81)

Answer

6(x - 3)^2(x^2 + 9)

Question 24

Factor completely: x^4 - 13x^2 + 36.

Accepted Answer

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

Answer

(x - 4)(x + 4)(x - 9)(x + 9)

Answer

(x - 6)(x + 6)(x - 1)(x + 1)

Answer

(x - 3)^2(x + 2)^2

Question 25

Factor completely: x^4 - 26x^2 + 25.

Accepted Answer

(x - 1)(x + 1)(x - 5)(x + 5)

Answer

(x - 1)(x + 1)(x - 25)(x + 25)

Answer

(x - 1)(x + 1)(x^2 + 25)

Answer

(x - 5)^2(x + 1)^2

Question 26

What is the first step in factoring 4x^3 - 16x^2 + 3x - 12?

Accepted Answer

group it as (4x^3 - 16x^2) + (3x - 12)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 4x

Question 27

Factor completely: x^3 + 3x^2 - 16x - 48.

Accepted Answer

(x + 3)(x - 4)(x + 4)

Answer

(x - 3)(x - 4)(x + 4)

Answer

(x + 3)(x - 4)^2

Answer

(x + 3)(x + 4)^2

Question 28

Factor completely: x^4 - 34x^2 + 225.

Accepted Answer

(x - 3)(x + 3)(x - 5)(x + 5)

Answer

(x - 9)(x + 9)(x - 25)(x + 25)

Answer

(x - 15)(x + 15)(x - 1)(x + 1)

Answer

(x - 5)^2(x + 3)^2

Question 29

Factor completely: x^4 - 45x^2 + 324.

Accepted Answer

(x - 3)(x + 3)(x - 6)(x + 6)

Answer

(x - 9)(x + 9)(x - 36)(x + 36)

Answer

(x - 18)(x + 18)(x - 1)(x + 1)

Answer

(x - 6)^2(x + 3)^2

Question 30

Factor completely: 6x^4 - 1536.

Accepted Answer

6(x - 4)(x + 4)(x^2 + 16)

Answer

6(x - 4)(x + 4)(x^2 - 16)

Answer

6(x - 16)(x + 16)(x^2 + 256)

Answer

6(x - 4)^2(x^2 + 16)

Question 31

Factor completely: 2x^4 - 512.

Accepted Answer

2(x - 4)(x + 4)(x^2 + 16)

Answer

2(x - 4)(x + 4)(x^2 - 16)

Answer

2(x - 16)(x + 16)(x^2 + 256)

Answer

2(x - 4)^2(x^2 + 16)

Question 32

Factor completely: x^4 - 17x^2 + 16.

Accepted Answer

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

Answer

(x - 1)(x + 1)(x - 16)(x + 16)

Answer

(x - 1)(x + 1)(x^2 + 16)

Answer

(x - 4)^2(x + 1)^2

Question 33

Factor completely: x^4 - 20x^2 + 64.

Accepted Answer

(x - 2)(x + 2)(x - 4)(x + 4)

Answer

(x - 4)(x + 4)(x - 16)(x + 16)

Answer

(x - 8)(x + 8)(x - 1)(x + 1)

Answer

(x - 4)^2(x + 2)^2

Question 34

What is the first step in factoring 4x^3 - 8x^2 + 3x - 6?

Accepted Answer

group it as (4x^3 - 8x^2) + (3x - 6)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 4x

Question 35

Factor completely: x^3 + 3x^2 - x - 3.

Accepted Answer

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

Answer

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

Answer

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

Answer

(x + 3)(x + 1)^2

Question 36

Factor completely: x^3 + 4x^2 - 9x - 36.

Accepted Answer

(x + 4)(x - 3)(x + 3)

Answer

(x - 4)(x - 3)(x + 3)

Answer

(x + 4)(x - 3)^2

Answer

(x + 4)(x + 3)^2

Question 37

Factor completely: x^3 + 2x^2 - x - 2.

Accepted Answer

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

Answer

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

Answer

(x + 2)(x - 1)^2

Answer

(x + 2)(x + 1)^2

Question 38

Factor completely: x^3 + 3x^2 - 4x - 12.

Accepted Answer

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

Answer

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

Answer

(x + 3)(x - 2)^2

Answer

(x + 3)(x + 2)^2

Question 39

What is the first step in factoring 3x^3 - 9x^2 + 7x - 21?

Accepted Answer

group it as (3x^3 - 9x^2) + (7x - 21)

Answer

rewrite it as a difference of two cubes

Answer

substitute u = x^2 to make it quadratic

Answer

divide every term by 3x

Question 40

Factor completely: x^3 + 5x^2 - 9x - 45.

Accepted Answer

(x + 5)(x - 3)(x + 3)

Answer

(x - 5)(x - 3)(x + 3)

Answer

(x + 5)(x - 3)^2

Answer

(x + 5)(x + 3)^2

BLASTROOM

BLASTROOM

BLASTROOM

Factoring Higher-Degree Polynomials

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Factoring Higher-Degree Polynomials

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner