Question 1

Solve the equation.
-$- 6 x ^ { 2 } = - 9 x - x ^ { 3 }$

Accepted Answer

A) 0, -3, -3 
B) -3, -3 
C) 0, 3, 3 
D) 3, 3 
A) 0, -3, -3 
B) -3, -3 
C) 0, 3, 3 
D) 3, 3

Question 2

Factor the four-term polynomial by grouping.
-3xy + 9x + 7y + 21

Accepted Answer

A) (3x + 3)(y + 7) 
B) (3x + y)(7y + 3) 
C) (3x + 7y)(y + 3) 
D) (3x + 7)(y + 3) 
A) (3x + 3)(y + 7) 
B) (3x + y)(7y + 3) 
C) (3x + 7y)(y + 3) 
D) (3x + 7)(y + 3)

Question 3

Solve the equation.
-5(x - 2)(x - 3)= 0

Accepted Answer

A) -2, -3 
B) 2, 3 
C) 0, 2, 3 
D) 5, 2, 3 
A) -2, -3 
B) 2, 3 
C) 0, 2, 3 
D) 5, 2, 3

Question 4

Factor the four-term polynomial by grouping.
-xy - 9yz + 12x - 108z

Accepted Answer

A) (y - 12)(x + 9z) 
B) (y - 9)(x + 12z) 
C) (y + 12)(x - 9z) 
D) (y + 9)(x - 12z) 
A) (y - 12)(x + 9z) 
B) (y - 9)(x + 12z) 
C) (y + 12)(x - 9z) 
D) (y + 9)(x - 12z)

Question 5

Factor the binomial completely.
-$x ^ { 4 } - 256$

Accepted Answer

A)  $\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 16 \right)$ 
B)  $\left( x ^ { 2 } + 16 \right) \left( x ^ { 2 } + 16 \right)$ 
C)  $\left( x ^ { 2 } + 16 \right) ( x + 4 ) ( x - 4 )$ 
D) prime 
A)  $\left( x ^ { 2 } - 16 \right) \left( x ^ { 2 } - 16 \right)$ 
B)  $\left( x ^ { 2 } + 16 \right) \left( x ^ { 2 } + 16 \right)$ 
C)  $\left( x ^ { 2 } + 16 \right) ( x + 4 ) ( x - 4 )$ 
D) prime

Question 6

Solve the equation.
-4x(4x - 7)(7x + 6)= 0

Accepted Answer

A)  $0 , \frac { 7 } { 4 } , - \frac { 6 } { 7 }$ 
B)  $0 , - \frac { 7 } { 4 } , \frac { 6 } { 7 }$ 
C)  $\frac { 7 } { 4 } , - \frac { 6 } { 7 }$ 
D)  $0 , \frac { 6 } { 7 } , - \frac { 7 } { 6 }$ 
A)  $0 , \frac { 7 } { 4 } , - \frac { 6 } { 7 }$ 
B)  $0 , - \frac { 7 } { 4 } , \frac { 6 } { 7 }$ 
C)  $\frac { 7 } { 4 } , - \frac { 6 } { 7 }$ 
D)  $0 , \frac { 6 } { 7 } , - \frac { 7 } { 6 }$

Question 7

Solve.
-A window washer accidentally drops a bucket from the top of a 64-foot building. The height h of the bucket after t seconds is given byn by $h = - 16 t ^ { 2 } + 64$ . When will the bucket hit the ground?

Accepted Answer

A) 2 sec 
B) 4 sec 
C) -2 sec 
D) 32 sec 
A) 2 sec 
B) 4 sec 
C) -2 sec 
D) 32 sec

Question 8

Factor a -1 from the polynomial.
--7 + y

Accepted Answer

A) -1(7 - y) 
B) -1(y + 7) 
C) -1(y - 7) 
D) -1(-y - 7) 
A) -1(7 - y) 
B) -1(y + 7) 
C) -1(y - 7) 
D) -1(-y - 7)

Question 9

Factor a -1 from the polynomial.
--y - 7

Accepted Answer

A) -1(-y - 7) 
B) -1(y - 7) 
C) -1(7 - y) 
D) -1(y + 7) 
A) -1(-y - 7) 
B) -1(y - 7) 
C) -1(7 - y) 
D) -1(y + 7)

Question 10

Factor the polynomial by grouping.
-$25 x + 35 x ^ { 2 } + 6 x ^ { 3 }$

Accepted Answer

A) 6x(x + 5)(x + 5) 
B) x(x + 5)(6x + 5) 
C) x(6x + 5)(x + 6) 
D) prime 
A) 6x(x + 5)(x + 5) 
B) x(x + 5)(6x + 5) 
C) x(6x + 5)(x + 6) 
D) prime

Question 11

Factor the binomial completely.
-$x ^ { 2 } - \frac { 1 } { 4 }$

Accepted Answer

A)  $\left( x + \frac { 1 } { 2 } \right) \left( \frac { 1 } { 2 } - x \right)$ 
B)  $\left( x + \frac { 1 } { 2 } \right) ^ { 2 }$ 
C)  $\left( x + \frac { 1 } { 2 } \right) \left( x - \frac { 1 } { 2 } \right)$ 
D)  $\left( x - \frac { 1 } { 2 } \right) ^ { 2 }$ 
A)  $\left( x + \frac { 1 } { 2 } \right) \left( \frac { 1 } { 2 } - x \right)$ 
B)  $\left( x + \frac { 1 } { 2 } \right) ^ { 2 }$ 
C)  $\left( x + \frac { 1 } { 2 } \right) \left( x - \frac { 1 } { 2 } \right)$ 
D)  $\left( x - \frac { 1 } { 2 } \right) ^ { 2 }$

Question 12

Factor the polynomial by grouping.
-$15 x ^ { 3 } + 38 x ^ { 2 } + 24 x$

Accepted Answer

A) x(3x + 4)(5x + 6) 
B) x(3x + 6)(5x + 4) 
C) 3x(x + 4)(5x + 6) 
D) prime 
A) x(3x + 4)(5x + 6) 
B) x(3x + 6)(5x + 4) 
C) 3x(x + 4)(5x + 6) 
D) prime

Question 13

Factor the binomial completely.
-$z ^ { 2 } s ^ { 2 } - 1$

Accepted Answer

A)  $( \mathrm { zs } - 1 ) ^ { 2 }$ 
B)  $( z s + 1 ) ^ { 2 }$ 
C) (zs + 1)(zs - 1) 
D) prime 
A)  $( \mathrm { zs } - 1 ) ^ { 2 }$ 
B)  $( z s + 1 ) ^ { 2 }$ 
C) (zs + 1)(zs - 1) 
D) prime

Question 14

Solve the equation.
-$4 x ^ { 2 } - 3 x - 7$ = 0

Accepted Answer

A)  $\frac { 4 } { 7 } , 1$ , 1 
B)  $\frac { 4 } { 7 } , 0$ 
C)  $\frac { 7 } { 4 } , - 1$ 1 
D)  $\frac { 4 } { 7 } , - 1$ 1 
A)  $\frac { 4 } { 7 } , 1$ , 1 
B)  $\frac { 4 } { 7 } , 0$ 
C)  $\frac { 7 } { 4 } , - 1$ 1 
D)  $\frac { 4 } { 7 } , - 1$ 1

Question 15

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-  $162 - 2 x ^ { 2 }$

Accepted Answer

A) 2(x + 9)(x - 9) 
B) 2(9 + x)(9 - x) 
C)  $2 ( x - 9 ) ^ { 2 }$ 
D) Prime 
A) 2(x + 9)(x - 9) 
B) 2(9 + x)(9 - x) 
C)  $2 ( x - 9 ) ^ { 2 }$ 
D) Prime

Question 16

Solve the equation.
-$x ^ { 2 } + 5 x = 66$

Accepted Answer

A) 11, 6 
B) -11, 6 
C) 11, -6 
D) -11, 1 
A) 11, 6 
B) -11, 6 
C) 11, -6 
D) -11, 1

Question 17

Solve.
-A triangle is 8 cm wider than it is tall. The area is 280 cm2. Find the width (length of the base). h + 8

Accepted Answer

A) 20 cm 
B) 8 cm 
C) 28 cm 
D) 29 cm 
A) 20 cm 
B) 8 cm 
C) 28 cm 
D) 29 cm

Question 18

Factor a -1 from the polynomial.
-- $- 17 x ^ { 3 } + x ^ { 2 } + 16$

Accepted Answer

A)  $- 1 \left( 16 x ^ { 3 } + x ^ { 2 } - 17 \right)$ 
B)  $- 1 \left( 17 x ^ { 3 } + x ^ { 2 } - 16 \right)$ 
C)  $- 1 \left( 17 x ^ { 3 } - x ^ { 2 } + 16 \right)$ 
D)  $- 1 \left( 17 x ^ { 3 } - x ^ { 2 } - 16 \right)$ 
A)  $- 1 \left( 16 x ^ { 3 } + x ^ { 2 } - 17 \right)$ 
B)  $- 1 \left( 17 x ^ { 3 } + x ^ { 2 } - 16 \right)$ 
C)  $- 1 \left( 17 x ^ { 3 } - x ^ { 2 } + 16 \right)$ 
D)  $- 1 \left( 17 x ^ { 3 } - x ^ { 2 } - 16 \right)$

Question 19

Solve.
-One leg of a right triangle is 21 inches longer than the smaller leg, and the hypotenuse is 24 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Accepted Answer

A) 12 in., 33 in., 36 in 
B) 14 in., 35 in., 40 in 
C) 15 in., 36 in., 39 in. 
D) 16 in., 37 in., 40 in 
A) 12 in., 33 in., 36 in 
B) 14 in., 35 in., 40 in 
C) 15 in., 36 in., 39 in. 
D) 16 in., 37 in., 40 in

Question 20

Solve the equation.
- $( x + 8 ) \left( x ^ { 2 } - 3 x + 2 \right) = 0$

Accepted Answer

A) -8, 2, 1 
B) -8 
C) 8 
D) 8, -2, -1 
A) -8, 2, 1 
B) -8 
C) 8 
D) 8, -2, -1

Solve the equation. - $- 6 x ^ { 2 } = - 9 x - x ^ { 3 }$

Factor the four-term polynomial by grouping. -3xy + 9x + 7y + 21

Solve the equation. -5(x - 2)(x - 3)= 0

Factor the four-term polynomial by grouping. -xy - 9yz + 12x - 108z

Factor the binomial completely. - $x ^ { 4 } - 256$

Solve the equation. -4x(4x - 7)(7x + 6)= 0

Solve. -A window washer accidentally drops a bucket from the top of a 64-foot building. The height h of the bucket after t seconds is given byn by $h = - 16 t ^ { 2 } + 64$ . When will the bucket hit the ground?

Factor a -1 from the polynomial. --7 + y

Factor a -1 from the polynomial. --y - 7

Factor the polynomial by grouping. - $25 x + 35 x ^ { 2 } + 6 x ^ { 3 }$

Factor the binomial completely. - $x ^ { 2 } - \frac { 1 } { 4 }$

Factor the polynomial by grouping. - $15 x ^ { 3 } + 38 x ^ { 2 } + 24 x$

Factor the binomial completely. - $z ^ { 2 } s ^ { 2 } - 1$

Solve the equation. - $4 x ^ { 2 } - 3 x - 7$ = 0

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $162 - 2 x ^ { 2 }$

Solve the equation. - $x ^ { 2 } + 5 x = 66$

Solve. -A triangle is 8 cm wider than it is tall. The area is 280 cm2. Find the width (length of the base). h + 8

Factor a -1 from the polynomial. -- $- 17 x ^ { 3 } + x ^ { 2 } + 16$

Solve. -One leg of a right triangle is 21 inches longer than the smaller leg, and the hypotenuse is 24 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Solve the equation. - $( x + 8 ) \left( x ^ { 2 } - 3 x + 2 \right) = 0$

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Exam 13: Factoring Polynomials

Solve the equation. - −6x2=−9x−x3- 6 x ^ { 2 } = - 9 x - x ^ { 3 }−6x2=−9x−x3