Simplifying Polynomials Worksheet

**Page 3**

21.

Factor: 3$x$^{2} + 12$x$ + 3$x$ + 12

a. | (3$x$ - 3)($x$ + 4) | ||

b. | (3$x$ + 3)($x$ + 4) | ||

c. | (3$x$ ^{2} +3)($x$ - 4) | ||

d. | None of the above |

[Original expression.]

= (3

[Group terms.]

= 3

[Factor each group.]

= (3

[Use distributive property.]

Correct answer : (2)

22.

Factor: $x$^{3} + 216

a. | ($x$ + 6)($x$ ^{2} + 6$x$ + 36) | ||

b. | ($x$ - 6)($x$ ^{2} - 6$x$ + 36) | ||

c. | ($x$ + 6)($x$ ^{2} - 6$x$ + 36) | ||

d. | None of the above |

[Original expression.]

=

[Write the terms as the sum of cubes.]

= (

[Use (

Correct answer : (3)

23.

Factor: 3$x$^{3} + 375

a. | 3(($x$ - 5)($x$ ^{2} + 5$x$ + 25)) | ||

b. | 3(($x$ + 5)($x$ ^{2} - 5$x$ + 25)) | ||

c. | 3(($x$ + 5)($x$ ^{2} + 5$x$ + 25) | ||

d. | None of the above |

[Original expression.]

3(

[Factor out the GCF.]

= 3(

[Write the terms inside the grouping symbols as the sum of cubes.]

= 3[(

[Use (

Correct answer : (2)

24.

Factor: $x$^{3} - 64

a. | $x$ - 4)($x$ ^{2} - 4$x$ + 16) | ||

b. | ($x$ - 4)($x$ ^{2} + 4$x$ + 16) | ||

c. | ($x$ + 4)($x$ ^{2} + 4$x$ + 16) | ||

d. | None of the above |

[Original expression.]

=

[Write the terms as the difference between cubes.]

= (

[Use (

Correct answer : (2)

25.

The length, width and height of a rectangular prism are ($x$ + 4), ($x$ - 1) and $x$, respectively. If the volume of the rectangular prism is 12 cubic units, then find the dimensions of the rectangular prism.

a. | 7 units, 6 units, 2 units | ||

b. | 6 units, 1 units, 2 units | ||

c. | 5 units, 1 units, 3 units | ||

d. | None of the above |

The volume of the rectangular prism in the question = 12cubic units and its length, width and height are (

12 =

[Write the equation.]

12 =

[Multiply.]

0 =

[Subtract 12 from each side.]

0 = (

[Group terms.]

0 =

[Use GCF to factor each group.]

0 = (

[Use distributive property.]

0 = (

[Factor the difference between two squares.]

[Evaluate

Since the dimension cannot be a negative value,

(

So, the dimensions of the rectangular prism are 6 units,1 unit and 2 units.

Correct answer : (2)