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Exam 6: Factoring Polynomials

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Question 31

Multiple Choice

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Factor out the GCF from the polynomial. - $10 m ^ { 9 } + 4 m ^ { 6 } + 4 m ^ { 3 }$

A) $2 \left( 5 m ^ { 9 } + 2 m ^ { 6 } + 2 m ^ { 3 } \right)$
B) $m ^ { 3 } \left( 10 m ^ { 6 } + 4 m ^ { 3 } + 4 \right)$
C) $2 m ^ { 3 } \left( 5 m ^ { 6 } + 2 m ^ { 3 } + 2 \right)$
D) $- 2 m ^ { 3 } \left( 5 m ^ { 6 } - 2 m ^ { 3 } - 2 \right)$

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Question 32

Multiple Choice

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Factor out the GCF from the polynomial. - $64 x ^ { 8 } y ^ { 9 } + 16 x ^ { 2 } y ^ { 4 } - 72 x ^ { 5 } y ^ { 2 }$

A) $8 x ^ { 2 } y ^ { 2 } \left( 8 x ^ { 6 } y ^ { 7 } + 2 y ^ { 2 } - 9 x ^ { 3 } \right)$
B) $x ^ { 2 } y ^ { 2 } \left( 64 x ^ { 6 } y ^ { 7 } + 16 y ^ { 2 } - 72 x ^ { 3 } \right)$
C) $8 \left( 8 x ^ { 8 } y ^ { 9 } + 2 x ^ { 2 } y ^ { 4 } - 9 x ^ { 5 } y ^ { 2 } \right)$
D) $8 x ^ { 2 } \left( 8 x ^ { 6 } y ^ { 9 } + 2 y ^ { 4 } - 9 x ^ { 3 } y ^ { 2 } \right)$

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Question 33

Multiple Choice

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Solve. -The side of a square equals the length of a rectangle. The width of the rectangle is 4 meters longer than its length. The sum of the areas of the square and the rectangle is 198 square centimeters. Find the side of the square.

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. $\begin{array} { l l l l } \text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \\\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \\\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }\end{array}$ -The ________ of a list of terms is the product of all common factors.

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $6 x ^ { 3 } - 60 x ^ { 2 } + 126 x$

Factor the sum or difference of two cubes. - $t ^ { 3 } + 8$

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. $\begin{array} { l l l l } \text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \\\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \\\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }\end{array}$ -By the zero factor property, if the product of two numbers is 0, then at least one of the numbers must be ________

Factor the trinomial by grouping. - $3 x ^ { 2 } + 11 x - 20$

Solve the equation. - $( x + 8 ) ( x + 1 ) = 44$

Factor the four-term polynomial by grouping. - $8 x ^ { 4 } - 20 x ^ { 2 } + 10 x ^ { 2 } - 25$

Factor completely. - $75 x ^ { 3 } - 110 x ^ { 2 } + 40 x$

Factor the trinomial by grouping. - $8 x ^ { 2 } - x - 34$

Solve. -The area of a circle is 144π square meters. Find its radius.

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $6 x ^ { 2 } - 18 x y - 24 y ^ { 2 }$

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be used more than once. $\begin{array} { l l l l } \text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \\\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \\\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }\end{array}$ -An equation that can be written in the form $a x ^ { 2 } + b x + c = 0$ (with a not 0 ) is called a_________

Factor the perfect square trinomial completely. - $x ^ { 2 } + 16 x y + 64 y ^ { 2 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $- x ^ { 2 } - 8 x + 48$

Factor the sum or difference of two cubes. - $512 p ^ { 3 + 1 }$

Factor completely. - $10 x ^ { 2 } + 11 x y - 6 y ^ { 2 }$

Find the GCF for the list. -12, 24, 27