Master Polynomial Factoring: Practice Quizzes and Study Guide

Question 1

Factor the polynomial: x³ - 8

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

(x + 2)(x² - 2x + 4)

Answer

(x - 8)(x² + 8x + 64)

Answer

(x + 8)(x² - 8x + 64)

Question 2

Factor the polynomial as a difference of squares of squares: x⁴ - 16

Accepted Answer

(x² - 4)(x² + 4)

Answer

(x - 4)(x³ + 4x² + 16x + 64)

Answer

(x + 4)(x³ - 4x² + 16x - 64)

Answer

(x - 2)(x + 2)(x² + 4)

Question 3

Factor the polynomial as a difference of squares of squares: x⁴ - 81

Accepted Answer

(x² - 9)(x² + 9)

Answer

(x - 9)(x³ + 9x² + 81x + 729)

Answer

(x + 9)(x³ - 9x² + 81x - 729)

Answer

(x - 3)(x + 3)(x² + 9)

Question 4

Factor the polynomial by difference of squares: 16x² - 9

Accepted Answer

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

Answer

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

Answer

(16x - 3)(x + 3)

Answer

(16x + 3)(x - 3)

Question 5

Factor the polynomial x² - 9.

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)²

Answer

(x - 3)²

Answer

The polynomial is prime.

Question 6

Factor the polynomial 6x² - 11x + 3 using the quadratic formula.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

Factor the polynomial 3x³ + 6x² - 9x.

Accepted Answer

3x(x² + 2x - 3)

Answer

x(3x² + 6x - 9)

Answer

3(x³ + 2x² - 3x)

Answer

The polynomial is prime.

Question 8

Factor the polynomial: **x² - 9**

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)²

Answer

(x + 3)²

Answer

Cannot be factored

Question 9

Factor the polynomial: **x³ - 8**

Accepted Answer

(x - 2)(x² + 2x + 4)

Answer

(x + 2)(x² - 2x + 4)

Answer

(x - 2)³

Answer

Cannot be factored

Question 10

Factor the polynomial: **x² + 6x + 8**

Accepted Answer

(x + 2)(x + 4)

Answer

(x - 2)(x + 4)

Answer

(x + 8)(x - 1)

Answer

Cannot be factored

Question 11

Factor the polynomial: **x² - 2xy + y²**

Accepted Answer

(x - y)(x + y)

Answer

(x - 2y)²

Answer

(x + 2y)²

Answer

Cannot be factored

Question 12

Factor the polynomial: **x³ - 2x² - 5x + 6**

Accepted Answer

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

Answer

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

Answer

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

Answer

Cannot be factored

Question 13

Factor the polynomial: **2x² - 5x + 2**

Accepted Answer

(2x - 1)(x - 2)

Answer

(2x + 1)(x - 2)

Answer

(2x - 1)(x + 2)

Answer

Cannot be factored

Question 14

Factor the polynomial: **x⁴ - 16**

Accepted Answer

(x - 2)(x + 2)(x² + 4)

Answer

(x - 4)(x + 4)(x² - 8)

Answer

(x - 2)²(x + 2)²

Answer

Cannot be factored

Question 15

Factor the polynomial: **x³ + 6x² + 9x**

Accepted Answer

x(x + 3)²

Answer

x(x - 3)²

Answer

(x + 3)(x² - 3x + 9)

Answer

Cannot be factored

Question 16

Which of the following is a special case of factoring polynomials that involves recognizing and factoring expressions that are perfect squares?

Accepted Answer

Factoring perfect squares

Answer

Factoring by grouping

Answer

Factoring by trial and error

Answer

Factoring trinomials

Question 17

Factor the polynomial x^4 - 16 using the quadratic formula.

Accepted Answer

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

Answer

(x^2 - 8)(x^2 + 8)

Answer

Cannot be factored using the quadratic formula

Question 18

Factor the following using grouping: 2x³ - 3x² - 11x + 6.

Accepted Answer

(2x - 3)(x² + 2x - 2)

Answer

(2x + 3)(x² - 2x - 2)

Answer

(2x - 3)(x² - 2x + 2)

Answer

(2x + 3)(x² + 2x + 2)

Question 19

Factor the polynomial: x² - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)

Answer

(x - 3)²

Answer

(x + 9)

Question 20

Factor the polynomial: x² - 25.

Accepted Answer

(x - 5)(x + 5)

Answer

Cannot be factored

Answer

(x - 25)(x + 1)

Answer

(x + 5)²

Question 21

Factor the polynomial: x⁴ + 16.

Accepted Answer

(x² + 4)(x² - 4)

Answer

(x + 4)(x - 4)

Answer

(x² + 4i)(x² - 4i)

Answer

(x + 4i)(x - 4i)

Question 22

Factor the polynomial: x³ - 8y³.

Accepted Answer

(x - 2y)(x² + 2xy + 4y²)

Answer

(x + 2y)(x² - 2xy + 4y²)

Answer

(x - 8y)(x² + 8xy + 64y²)

Answer

(x + 8y)(x² - 8xy + 64y²)

Question 23

Factor the polynomial: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x + 1)(x - 9)

Answer

(x - 3)^2

Answer

(x - 1)(x + 9)

Question 24

Factor the polynomial: x^4 - 16

Accepted Answer

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

Answer

(x - 4)^4

Answer

(x + 4)^4

Answer

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

Question 25

Factor the polynomial: 2x^3 + 6x^2 - 8x

Accepted Answer

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

Answer

x(2x^2 + 6x - 8)

Answer

x^2(2x + 6 - 8)

Answer

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

Question 26

Factor the polynomial: 2x^2 + 4x - 6

Accepted Answer

2(x + 3)(x - 1)

Answer

2(x^2 + 2x - 3)

Answer

2x(x + 3 - 1)

Answer

(2x + 6)(x - 1)

Question 27

Which of the following is NOT a method for factoring polynomials?

Accepted Answer

Subtraction

Answer

Factoring by grouping

Answer

Difference of squares

Answer

Using the quadratic formula

Question 28

Factor the polynomial: x^2 - 4

Accepted Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

x(x - 4)

Answer

(x + 4)(x - 4)

Question 29

Factor the polynomial: 4x^2 - 12x + 9

Accepted Answer

(2x - 3)^2

Answer

(4x + 3)(x - 3)

Answer

2x(2x - 9)

Question 30

Factor the polynomial: 3x^2 - 10x + 3

Accepted Answer

(3x - 1)(x - 3)

Answer

(x - 1)(3x - 3)

Answer

(3x + 1)(x - 3)

Question 31

Factor the polynomial: x^3 - 27

Accepted Answer

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

Answer

x(x^2 + 9)

Answer

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

Answer

Cannot be factored

Question 32

Factor the trinomial: x² + 5x + 6

Accepted Answer

(x + 2)(x + 3)

Answer

(x + 1)(x + 5)

Answer

(x + 1)(x + 6)

Answer

(x - 2)(x - 3)

Question 33

Which of the following is a factor of the polynomial 4x² - 9?

Accepted Answer

(2x - 3)

Answer

(4x - 3)

Answer

(x - 3)

Answer

(2x + 3)

Question 34

Factor by grouping: 2xy + 3x + 4y + 6

Accepted Answer

(2y + 3)(x + 2)

Answer

(2y + 3)(x - 2)

Answer

(2y - 3)(x + 2)

Answer

(2y + 3)(x + 1)