Question 1

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$8 + 7 x + x ^ { 2 }$

Accepted Answer

A) (x + 4)(x + 2) 
B) (x + 8)(x - 1) 
C) (x + 8)(x + 1) 
D) prime 
A) (x + 4)(x + 2) 
B) (x + 8)(x - 1) 
C) (x + 8)(x + 1) 
D) prime

Question 2

Find the GCF for the list.
-$x ^ { 2 } , x ^ { 3 } , x ^ { 4 }$

Accepted Answer

A) x 
B)  $x ^ { 2 }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 9 }$ 
A) x 
B)  $x ^ { 2 }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 9 }$

Question 3

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-9(a + 3)- y(a + 3)

Accepted Answer

A) (a + 3)(9 + y) 
B) (a + 3)(9 - y) 
C) (a - 3)(y - 9) 
D) Prime 
A) (a + 3)(9 + y) 
B) (a + 3)(9 - y) 
C) (a - 3)(y - 9) 
D) Prime

Question 4

Factor the trinomial completely.
-9 $9 p ^ { 4 } - 42 p ^ { 3 } + 49 p ^ { 2 }$

Accepted Answer

A)  $p ^ { 2 } ( 3 p - 7 ) ( 3 p + 7 )$ 
B)  $p ^ { 2 } ( 3 p + 7 ) ^ { 2 }$ 
C)  $p ^ { 2 } ( 3 p - 7 ) ^ { 2 }$ 
D)  $p ^ { 2 } ( 9 p + 1 ) ( p + 49 )$ 
A)  $p ^ { 2 } ( 3 p - 7 ) ( 3 p + 7 )$ 
B)  $p ^ { 2 } ( 3 p + 7 ) ^ { 2 }$ 
C)  $p ^ { 2 } ( 3 p - 7 ) ^ { 2 }$ 
D)  $p ^ { 2 } ( 9 p + 1 ) ( p + 49 )$

Question 5

Factor the four-term polynomial by grouping.
-2x + 8 + xy + 4y

Accepted Answer

A) (x + 4)(2 + y) 
B) (x + 4y)(2 + y) 
C) (y + 4)(2x + y) 
D) (y + 4)(x + 2) 
A) (x + 4)(2 + y) 
B) (x + 4y)(2 + y) 
C) (y + 4)(2x + y) 
D) (y + 4)(x + 2)

Question 6

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$2 x ^ { 3 } y ^ { 5 } + 2 x ^ { 2 } y ^ { 5 } - 12 x y ^ { 5 }$

Accepted Answer

A)  $y ^ { 5 } \left( 2 x ^ { 2 } + 4 x \right) ( x - 3 )$ 
B)  $2 x y ^ { 5 } ( x + 2 ) ( x - 3 )$ 
C)  $2 x y ^ { 5 } ( x - 2 ) ( x + 3 )$ 
D) prime 
A)  $y ^ { 5 } \left( 2 x ^ { 2 } + 4 x \right) ( x - 3 )$ 
B)  $2 x y ^ { 5 } ( x + 2 ) ( x - 3 )$ 
C)  $2 x y ^ { 5 } ( x - 2 ) ( x + 3 )$ 
D) prime

Question 7

Solve.
-Within a group of n people, the number of possible handshakes, N, is given byby $N = \frac { 1 } { 2 } \left( n ^ { 2 } - n \right)$ n). How many handshakes are possible at a meeting if 18 people are present?

Accepted Answer

A) 306 handshakes 
B) 144 handshakes 
C) 153 handshakes 
D) 171 handshakes 
A) 306 handshakes 
B) 144 handshakes 
C) 153 handshakes 
D) 171 handshakes

Question 8

Factor the trinomial completely.
-$20 y ^ { 2 } - 31 y + 12$

Accepted Answer

A) (20y + 3)(y + 4) 
B) (4y + 3)(5y + 4) 
C) (4y - 3)(5y - 4) 
D) prime 
A) (20y + 3)(y + 4) 
B) (4y + 3)(5y + 4) 
C) (4y - 3)(5y - 4) 
D) prime

Question 9

Factor the polynomial by grouping.
-$4 x ^ { 2 } - 4 x - 35$

Accepted Answer

A) (2x - 7)(2x + 5) 
B) (2x + 7)(2x - 5) 
C) (2x - 7)(x + 5) 
D) prime 
A) (2x - 7)(2x + 5) 
B) (2x + 7)(2x - 5) 
C) (2x - 7)(x + 5) 
D) prime

Question 10

Factor the trinomial completely.
-$20 x ^ { 2 } + 27 x + 9$

Accepted Answer

A) (4x - 3)(5x - 3) 
B) (20x + 3)(x + 3) 
C) (4x + 3)(5x + 3) 
D) prime 
A) (4x - 3)(5x - 3) 
B) (20x + 3)(x + 3) 
C) (4x + 3)(5x + 3) 
D) prime

Question 11

Factor out the GCF from the polynomial.
-$6 x ^ { 7 } - 48 x ^ { 5 }$

Accepted Answer

A)  $6 x ^ { 6 } ( x - 8 x )$ 
B)  $6 \left( x ^ { 7 } - 8 x ^ { 5 } \right)$ 
C)  $x ^ { 7 } \left( 6 x ^ { 2 } - 48 \right)$ 
D)  $6 x ^ { 5 } \left( x ^ { 2 } - 8 \right)$ 
A)  $6 x ^ { 6 } ( x - 8 x )$ 
B)  $6 \left( x ^ { 7 } - 8 x ^ { 5 } \right)$ 
C)  $x ^ { 7 } \left( 6 x ^ { 2 } - 48 \right)$ 
D)  $6 x ^ { 5 } \left( x ^ { 2 } - 8 \right)$

Question 12

Factor the polynomial by grouping.
-$7 x ^ { 2 } + 17 x - 12$

Accepted Answer

A) (x + 3)(7x - 4) 
B) (x - 3)(7x + 4) 
C) (x - 4)(7x + 3) 
D) prime 
A) (x + 3)(7x - 4) 
B) (x - 3)(7x + 4) 
C) (x - 4)(7x + 3) 
D) prime

Question 13

Solve the equation.
-(x - 6)(x + 5)= 0

Accepted Answer

A) 6, 5 
B) 6, -6, 5, -5 
C) -6, 5 
D) 6, -5 
A) 6, 5 
B) 6, -6, 5, -5 
C) -6, 5 
D) 6, -5

Question 14

Factor the binomial completely.
-$r ^ { 20 } - s ^ { 2 }$

Accepted Answer

A)  $\left( \mathrm { r } ^ { 10 } - \mathrm { s } \right) ^ { 2 }$ 
B)  $\left( \mathrm { r } ^ { 10 } + \mathrm { s } \right) ^ { 2 }$ 
C)  $\left( r ^ { 10 } + s \right) \left( r ^ { 10 } - s \right)$ 
D) prime 
A)  $\left( \mathrm { r } ^ { 10 } - \mathrm { s } \right) ^ { 2 }$ 
B)  $\left( \mathrm { r } ^ { 10 } + \mathrm { s } \right) ^ { 2 }$ 
C)  $\left( r ^ { 10 } + s \right) \left( r ^ { 10 } - s \right)$ 
D) prime

Question 15

Find the GCF for the list.
-$64 a ^ { 9 } b ^ { 3 } c ^ { 7 } , 40 a ^ { 6 } b ^ { 9 }$

Accepted Answer

A)  $8 a ^ { 9 } b ^ { 9 }$ 
B)  $4 a ^ { 6 } b ^ { 3 }$ 
C)  $8 a ^ { 6 } b ^ { 3 }$ 
D)  $8 a ^ { 6 } b ^ { 3 } c ^ { 7 }$ 
A)  $8 a ^ { 9 } b ^ { 9 }$ 
B)  $4 a ^ { 6 } b ^ { 3 }$ 
C)  $8 a ^ { 6 } b ^ { 3 }$ 
D)  $8 a ^ { 6 } b ^ { 3 } c ^ { 7 }$

Question 16

Factor the trinomial completely.
-$x ^ { 4 } - 10 x ^ { 2 } + 25$

Accepted Answer

A)  $\left( x ^ { 2 } - 10 \right) \left( x ^ { 2 } + 10 \right)$ 
B)  $\left( x ^ { 2 } + 5 \right) ^ { 2 }$ 
C)  $\left( x ^ { 2 } - 5 \right) ^ { 2 }$ 
D)  $\left( x ^ { 2 } - 5 \right) \left( x ^ { 2 } + 5 \right)$ 
A)  $\left( x ^ { 2 } - 10 \right) \left( x ^ { 2 } + 10 \right)$ 
B)  $\left( x ^ { 2 } + 5 \right) ^ { 2 }$ 
C)  $\left( x ^ { 2 } - 5 \right) ^ { 2 }$ 
D)  $\left( x ^ { 2 } - 5 \right) \left( x ^ { 2 } + 5 \right)$

Question 17

Find the GCF for the list.
-16, 10

Accepted Answer

A) 4 
B) 1 
C) 2 
D) 10 
A) 4 
B) 1 
C) 2 
D) 10

Question 18

Find the GCF for the list.
-$7 b ^ { 4 } \cdot 7 b ^ { 3 } k ^ { 6 } \cdot 3 b ^ { 4 }$

Accepted Answer

A)  $b ^ { 3 }$ 
B)  $7 b ^ { 3 }$ 
C)  $7 b ^ { 3 } k ^ { 6 }$ 
D)  $b ^ { 3 } k ^ { 6 }$ 
A)  $b ^ { 3 }$ 
B)  $7 b ^ { 3 }$ 
C)  $7 b ^ { 3 } k ^ { 6 }$ 
D)  $b ^ { 3 } k ^ { 6 }$

Question 19

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

Accepted Answer

A) (x + 4y)(x - 2y) 
B) (x - 4y)(x + y) 
C) (x - 4y)(x + 2y) 
D) Prime 
A) (x + 4y)(x - 2y) 
B) (x - 4y)(x + y) 
C) (x - 4y)(x + 2y) 
D) Prime

Question 20

Factor the trinomial completely.
-$x ^ { 2 } + 8 x + 16$

Accepted Answer

A) (x + 4)(x - 4) 
B) (x + 8)(x - 8) 
C)  $( x + 4 ) ^ { 2 }$ 
D)  $( x - 4 ) ^ { 2 }$ 
A) (x + 4)(x - 4) 
B) (x + 8)(x - 8) 
C)  $( x + 4 ) ^ { 2 }$ 
D)  $( x - 4 ) ^ { 2 }$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $8 + 7 x + x ^ { 2 }$

Find the GCF for the list. - $x ^ { 2 } , x ^ { 3 } , x ^ { 4 }$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." -9(a + 3)- y(a + 3)

Factor the trinomial completely. -9 $9 p ^ { 4 } - 42 p ^ { 3 } + 49 p ^ { 2 }$

Factor the four-term polynomial by grouping. -2x + 8 + xy + 4y

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 3 } y ^ { 5 } + 2 x ^ { 2 } y ^ { 5 } - 12 x y ^ { 5 }$

Solve. -Within a group of n people, the number of possible handshakes, N, is given byby $N = \frac { 1 } { 2 } \left( n ^ { 2 } - n \right)$ n). How many handshakes are possible at a meeting if 18 people are present?

Factor the trinomial completely. - $20 y ^ { 2 } - 31 y + 12$

Factor the polynomial by grouping. - $4 x ^ { 2 } - 4 x - 35$

Factor the trinomial completely. - $20 x ^ { 2 } + 27 x + 9$

Factor out the GCF from the polynomial. - $6 x ^ { 7 } - 48 x ^ { 5 }$

Factor the polynomial by grouping. - $7 x ^ { 2 } + 17 x - 12$

Solve the equation. -(x - 6)(x + 5)= 0

Factor the binomial completely. - $r ^ { 20 } - s ^ { 2 }$

Find the GCF for the list. - $64 a ^ { 9 } b ^ { 3 } c ^ { 7 } , 40 a ^ { 6 } b ^ { 9 }$

Factor the trinomial completely. - $x ^ { 4 } - 10 x ^ { 2 } + 25$

Find the GCF for the list. -16, 10

Find the GCF for the list. - $7 b ^ { 4 } \cdot 7 b ^ { 3 } k ^ { 6 } \cdot 3 b ^ { 4 }$

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

Factor the trinomial completely. - $x ^ { 2 } + 8 x + 16$

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Exam 13: Factoring Polynomials

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 8+7x+x28 + 7 x + x ^ { 2 }8+7x+x2

Find the GCF for the list. - x2,x3,x4x ^ { 2 } , x ^ { 3 } , x ^ { 4 }x2,x3,x4