Simplifying Polynomials Worksheet

**Page 1**

1.

Find the GCF of 40$x$^{3} and 48$x$^{2}.

a. | 3$x$ ^{2} | ||

b. | 8$x$ ^{2} | ||

c. | 8$x$ | ||

d. | 13$x$ ^{2} |

[Write the factors.]

48

[Write the factors.]

GCF = 8 ×

[Multiply the common factors.]

The GCF of 40

Correct answer : (2)

2.

Factor the GCF out of 28$x$^{3} - 35$x$^{2}.

a. | 5$x$ ^{2}(4$x$ + 7) | ||

b. | 7$x$ ^{2}(4$x$ + 5) | ||

c. | 5$x$ ^{2}(4$x$ - 7) | ||

d. | 7$x$ ^{2}(4$x$ - 5) |

[Write the factors.]

35

[Write the factors.]

GCF = 7 ×

[Multiply the common factors.]

28

[Original expression.]

= 7

[Use distributive property to factor out the greatest common factor from each term.]

Correct answer : (4)

3.

Factor 4$x$^{3} + 20$x$^{2} + 16$x$ completely.

a. | 4$x$($x$ ^{2} - 5$x$ + 4) | ||

b. | $x$($x$ ^{2} + 5$x$ + 4) | ||

c. | $x$(x ^{2} - 5x + 4) | ||

d. | 4$x$($x$ ^{2} + 5$x$ + 4) |

4

[Write the factors.]

20

[Write the factors.]

16

[Write the factors.]

GCF = 4 x

[Multiply the common factors.]

4

[Original expression.]

= 4

[Use the distributive property to factor out the greatest common factor from each term.]

Correct answer : (4)

4.

Factor: 5$x$^{3} - 6$x$^{2} - 45$x$ + 54

a. | (-5x - 6)(x + 3)(x - 3) | ||

b. | (5x - 6)(x + 3)(x - 3) | ||

c. | (5x - 6)(x + 3)(- x - 3) | ||

d. | (5x + 6)(x + 3)(x - 3) |

[Group the terms.]

=

[Factor out the GCF of each group.]

= (5

[Use distributive property.]

= (5

[Use difference between two squares pattern to factor.]

Correct answer : (2)

5.

Factor: 3$x$^{3} + $x$^{2} - 3$x$ - 1

a. | (3$x$ - 1)($x$ + 1)($x$ - 1) | ||

b. | (- 3$x$ + 1)($x$ + 1)($x$ - 1) | ||

c. | (3$x$ + 1)($x$ + 1)($x$ - 1) | ||

d. | None of the above |

[Group the terms.]

=

[Factor out GCF of each group.]

= (3

[Use distributive property.]

= (3

[Use difference between two squares pattern to factor.]

Correct answer : (3)

6.

Factor the GCF out of 5$x$^{3} + 25$x$^{2} + 25$x$.

a. | 5x(x ^{2} + 5x + 5) | ||

b. | x(5x ^{2} + 5x + 5) | ||

c. | 5x(x ^{2} + 5x + 5) | ||

d. | 5x(x ^{2} + 5x + 5) |

5

[Write the factors.]

25

[Write the factors.]

25

[Write the factors.]

GCF = 5 x

[Multiply the common factors.]

5

[Original expression.]

= 5

[Use the distributive property to factor out the greatest common factor from each term.]

Correct answer : (3)

7.

Factor the GCF out of 27$a$^{3} + 81$a$.

a. | $a$(27$a$ ^{2} + 3) | ||

b. | -27$a$($a$ ^{2} + 3) | ||

c. | 3$a$($a$ ^{2} + 27) | ||

d. | 27$a$($a$ ^{2} + 3) |

[Write the factors of 27

81

[Write the factors of 81

The GCF of two or more numbers is the product of their common factors.

The GCF of 27

27

[Original expression.]

= 27

[Use the distributive property to factor out the greatest common factor from each term.]

Correct answer : (4)

8.

Find the GCF of 5$a$^{2}, 45$a$, 65.

a. | 13 | ||

b. | 10 | ||

c. | 9 | ||

d. | 5 |

[Write the factors of 5

45

[Write the factors of 45

65 = 5 × 13

[Write the factors of 65.]

The GCF of two or more numbers is the product of their common factors.

The GCF of 5

Correct answer : (4)

9.

Find the GCF of 2$a$^{3}, 4$a$^{2}, 16$a$^{5}.

a. | 3$a$ ^{2} | ||

b. | 2$a$ ^{2} | ||

c. | $a$ ^{2} | ||

d. | None of the above |

[Write the factors of 2

4

[Write the factors of 4

16

[Write the factors of 16

The GCF of two or more numbers is the product of their common factors.

The GCF of 2

Correct answer : (2)

10.

Factor: - 2$a$^{2} - 8$a$ - 12

a. | -2($a$ ^{2} + 4$a$ - 6) | ||

b. | -2($a$ ^{2} + 4$a$ + 6) | ||

c. | -2($a$ ^{2} - 4$a$ - 6) | ||

d. | -4($a$ ^{2} - 4$a$ - 6) |

[Write the factors of -2

-8

[Write the factors of -8

-12 = -1 x 2 x 2 x 3

[Write the factors of -12.]

The GCF of two or more numbers is the product of their common factors.

The GCF of -2

-2

[Use the distributive property to factor out the greatest common factor from each term.]

Correct answer : (2)