Question 1

Solve the equation.
-$x ^ { 2 } - 64 = 63 x$

Accepted Answer

A) -8, 8 
B) 1, -64 
C) -1, 64 
D) -8, -8 
A) -8, 8 
B) 1, -64 
C) -1, 64 
D) -8, -8

Question 2

Solve.
-Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 4 kilometers an hour faster than the other. If after one hour the vehicles are 20 kilometers apart, find the
Rate of each vehicle.

Accepted Answer

A) Slower vehicle: -16 km/hr; faster vehicle: -12 km/hr 
B) Slower vehicle: 12 km/hr; faster vehicle: 16 km/hr 
C) Slower vehicle: 8 km/hr; faster vehicle: 12 km/hr 
D) Slower vehicle: 16 km/hr; faster vehicle: 20 km/hr 
A) Slower vehicle: -16 km/hr; faster vehicle: -12 km/hr 
B) Slower vehicle: 12 km/hr; faster vehicle: 16 km/hr 
C) Slower vehicle: 8 km/hr; faster vehicle: 12 km/hr 
D) Slower vehicle: 16 km/hr; faster vehicle: 20 km/hr

Question 3

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$6 y ^ { 2 } + 30 y + 36$

Accepted Answer

A) (6y + 2)(y + 3) 
B) 6(y - 2)(y - 3) 
C) (y + 2)(6y + 18) 
D) 6(y + 2)(y + 3) 
A) (6y + 2)(y + 3) 
B) 6(y - 2)(y - 3) 
C) (y + 2)(6y + 18) 
D) 6(y + 2)(y + 3)

Question 4

Factor out the GCF from the polynomial.
-$48 x ^ { 9 } y ^ { 6 } + 48 x ^ { 2 } y ^ { 4 } - 80 x ^ { 6 } y ^ { 2 }$

Accepted Answer

A) 16 $16 x ^ { 2 } \left( 3 x ^ { 7 } y ^ { 6 } + 3 y ^ { 4 } - 5 x ^ { 4 } y ^ { 2 } \right)$ 
B) 16(3x9y6 + 3x2y4 - 5x6y2) 
C)  $16 x ^ { 2 } y ^ { 2 } \left( 3 x ^ { 7 } y ^ { 4 } + 3 y ^ { 2 } - 5 x ^ { 4 } \right)$ 
D) x2y2(48x7y4 + 48y2 - 80x4) 
A) 16 $16 x ^ { 2 } \left( 3 x ^ { 7 } y ^ { 6 } + 3 y ^ { 4 } - 5 x ^ { 4 } y ^ { 2 } \right)$ 
B) 16(3x9y6 + 3x2y4 - 5x6y2) 
C)  $16 x ^ { 2 } y ^ { 2 } \left( 3 x ^ { 7 } y ^ { 4 } + 3 y ^ { 2 } - 5 x ^ { 4 } \right)$ 
D) x2y2(48x7y4 + 48y2 - 80x4)

Question 5

Factor the four-term polynomial by grouping.
-$12 x ^ { 4 } - 9 x ^ { 2 } - 8 x ^ { 2 } + 6$

Accepted Answer

A)  $\left( 3 x ^ { 4 } - 2 \right) ( 4 x - 3 )$ 
B)  $\left( 3 x ^ { 2 } + 2 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
C)  $\left( 12 x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 3 \right)$ 
D)  $\left( 3 x ^ { 2 } - 2 \right) \left( 4 x ^ { 2 } - 3 \right)$ 
A)  $\left( 3 x ^ { 4 } - 2 \right) ( 4 x - 3 )$ 
B)  $\left( 3 x ^ { 2 } + 2 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
C)  $\left( 12 x ^ { 2 } + 2 \right) \left( x ^ { 2 } + 3 \right)$ 
D)  $\left( 3 x ^ { 2 } - 2 \right) \left( 4 x ^ { 2 } - 3 \right)$

Question 6

Solve.
-A window washer is suspended 37 feet below the roof of a 985-foot-tall building. If the window washer drops an object from this height, the object's height h after t seconds is given by the equations is given by the equation $h = - 16 t ^ { 2 } + 948$ . Find ho Find how Many seconds pass before the object reaches the ground. Round to the nearest hundredth of a second when
Necessary.

Accepted Answer

A) 7.85 sec 
B) 7.55 sec 
C) 7.7 sec 
D) 59.25 sec 
A) 7.85 sec 
B) 7.55 sec 
C) 7.7 sec 
D) 59.25 sec

Question 7

Factor the four-term polynomial by grouping.
-$x ^ { 3 } + 2 x ^ { 2 } + x + 2$

Accepted Answer

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

Question 8

Factor out the GCF from the polynomial.
-$11 x ^ { 4 } + 17$

Accepted Answer

A)   $11 \left( x ^ { 4 } + 187 \right)$ 
B)   $11 \left( x ^ { 4 } + \frac { 17 } { 11 } \right)$ 
C)  $11 \left( x ^ { 4 } + 17 \right)$ 
D) No common factor 
A)   $11 \left( x ^ { 4 } + 187 \right)$ 
B)   $11 \left( x ^ { 4 } + \frac { 17 } { 11 } \right)$ 
C)  $11 \left( x ^ { 4 } + 17 \right)$ 
D) No common factor

Question 9

Solve the equation.
-x(x - 3)= 70

Accepted Answer

A) 7, 10 
B) 7, -10 
C) -7, 10 
D) 0, 3 
A) 7, 10 
B) 7, -10 
C) -7, 10 
D) 0, 3

Question 10

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$a ^ { 3 } b ^ { 2 } + 5 a ^ { 2 } b - 6 a$

Accepted Answer

A)  $a ^ { 5 } ( b - 1 ) ( b + 6 )$ 
B)  $a \left( a ^ { 2 } b ^ { 2 } + 5 a b - 6 \right)$ 
C) a(ab - 1)(ab + 6) 
D) a(ab + 1)(ab - 6) 
A)  $a ^ { 5 } ( b - 1 ) ( b + 6 )$ 
B)  $a \left( a ^ { 2 } b ^ { 2 } + 5 a b - 6 \right)$ 
C) a(ab - 1)(ab + 6) 
D) a(ab + 1)(ab - 6)

Question 11

Factor the four-term polynomial by grouping.
-7y - 77 + xy - 11x

Accepted Answer

A) (x - 11)(7y + x) 
B) (y - 11x)(7 + x) 
C) (y - 11)(7 + x) 
D) (x - 11)(y + 7) 
A) (x - 11)(7y + x) 
B) (y - 11x)(7 + x) 
C) (y - 11)(7 + x) 
D) (x - 11)(y + 7)

Question 12

Factor the trinomial completely.
-$7 x ^ { 2 } + 17 x - 12$

Accepted Answer

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

Question 13

Solve.
-If the sides of a square are increased by 2 meters, the area becomes 36 square meters. Find the length of a side of the original square.

Accepted Answer

A) 2 m 
B) 6 m 
C) 8 m 
D) 4 m 
A) 2 m 
B) 6 m 
C) 8 m 
D) 4 m

Question 14

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 4 } - 8 x ^ { 2 } - 33$

Accepted Answer

A)  $\left( x ^ { 2 } + 11 \right) \left( x ^ { 2 } - 3 \right)$ 
B)  $\left( x ^ { 2 } - 33 \right) \left( x ^ { 2 } + 1 \right)$ 
C)  $\left( x ^ { 2 } - 11 \right) \left( x ^ { 2 } + 3 \right)$ 
D) prime 
A)  $\left( x ^ { 2 } + 11 \right) \left( x ^ { 2 } - 3 \right)$ 
B)  $\left( x ^ { 2 } - 33 \right) \left( x ^ { 2 } + 1 \right)$ 
C)  $\left( x ^ { 2 } - 11 \right) \left( x ^ { 2 } + 3 \right)$ 
D) prime

Question 15

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$a ^ { 2 } - 4 a b - 12 b ^ { 2 }$

Accepted Answer

A) (a + 2b)(a - 6b) 
B) (a - 2b)(a + b) 
C) (a - 2b)(a + 6b) 
D) prime 
A) (a + 2b)(a - 6b) 
B) (a - 2b)(a + b) 
C) (a - 2b)(a + 6b) 
D) prime

Question 16

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

Accepted Answer

A) (x + 1)(x - 12) 
B) (x - 4)(x + 3) 
C) (x - 3)(x + 4) 
D) prime 
A) (x + 1)(x - 12) 
B) (x - 4)(x + 3) 
C) (x - 3)(x + 4) 
D) prime

Question 17

Find the GCF for the list.
-28, 10, 35

Accepted Answer

A) 1 
B) 2 
C) 5 
D) 7 
A) 1 
B) 2 
C) 5 
D) 7

Question 18

Determine whether the trinomial is a perfect square trinomial.
-$x ^ { 2 } - 10 x + 100$

Accepted Answer

A) True 
 B)False

Question 19

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 3 } + 2 x ^ { 2 } - 35 x$

Accepted Answer

A)  $x \left( x ^ { 2 } + 2 x - 35 \right)$ 
B) x(x - 7)(x - 5) 
C) x(x + 7)(x + 5) 
D) x(x + 7)(x - 5) 
A)  $x \left( x ^ { 2 } + 2 x - 35 \right)$ 
B) x(x - 7)(x - 5) 
C) x(x + 7)(x + 5) 
D) x(x + 7)(x - 5)

Question 20

Factor the trinomial completely.
-$10 x ^ { 2 } + 24 x + 8$

Accepted Answer

A) (2x + 2)(5x + 4) 
B) (x + 2)(10x + 4) 
C) (5x - 2)(2x - 4) 
D) (5x + 2)(2x + 4) 
A) (2x + 2)(5x + 4) 
B) (x + 2)(10x + 4) 
C) (5x - 2)(2x - 4) 
D) (5x + 2)(2x + 4)

Solve the equation. - $x ^ { 2 } - 64 = 63 x$

Solve. -Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 4 kilometers an hour faster than the other. If after one hour the vehicles are 20 kilometers apart, find the Rate of each vehicle.

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $6 y ^ { 2 } + 30 y + 36$

Factor out the GCF from the polynomial. - $48 x ^ { 9 } y ^ { 6 } + 48 x ^ { 2 } y ^ { 4 } - 80 x ^ { 6 } y ^ { 2 }$

Factor the four-term polynomial by grouping. - $12 x ^ { 4 } - 9 x ^ { 2 } - 8 x ^ { 2 } + 6$

Factor the four-term polynomial by grouping. - $x ^ { 3 } + 2 x ^ { 2 } + x + 2$

Factor out the GCF from the polynomial. - $11 x ^ { 4 } + 17$

Solve the equation. -x(x - 3)= 70

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $a ^ { 3 } b ^ { 2 } + 5 a ^ { 2 } b - 6 a$

Factor the four-term polynomial by grouping. -7y - 77 + xy - 11x

Factor the trinomial completely. - $7 x ^ { 2 } + 17 x - 12$

Solve. -If the sides of a square are increased by 2 meters, the area becomes 36 square meters. Find the length of a side of the original square.

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 4 } - 8 x ^ { 2 } - 33$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $a ^ { 2 } - 4 a b - 12 b ^ { 2 }$

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

Find the GCF for the list. -28, 10, 35

Determine whether the trinomial is a perfect square trinomial. - $x ^ { 2 } - 10 x + 100$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 3 } + 2 x ^ { 2 } - 35 x$

Factor the trinomial completely. - $10 x ^ { 2 } + 24 x + 8$

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Exam 13: Factoring Polynomials

Solve the equation. - x2−64=63xx ^ { 2 } - 64 = 63 xx2−64=63x