Question 1

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$5 x ^ { 2 } y + 5 x y - 25 y$

Accepted Answer

A)  $y \left( 5 x ^ { 2 } + 5 x - 25 \right)$ 
B) 5y(x + 5)(x - 1) 
C) 5(x + 5y)(x - 1) 
D)  $5 y \left( x ^ { 2 } + x - 5 \right)$ 
A)  $y \left( 5 x ^ { 2 } + 5 x - 25 \right)$ 
B) 5y(x + 5)(x - 1) 
C) 5(x + 5y)(x - 1) 
D)  $5 y \left( x ^ { 2 } + x - 5 \right)$

Question 2

Solve the equation.
-$y ^ { 3 } + 10 y ^ { 2 } + 25 y = 0$

Accepted Answer

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

Question 3

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$y ^ { 2 } - 2 y - 80$

Accepted Answer

A) (y + 10)(y - 8) 
B) (y - 80)(y + 1) 
C) (y - 10)(y + 8) 
D) Prime 
A) (y + 10)(y - 8) 
B) (y - 80)(y + 1) 
C) (y - 10)(y + 8) 
D) Prime

Question 4

Solve the equation.
-(x - 3)(3x + 15)= 0

Accepted Answer

A)  $- \frac { 1 } { 5 } , \frac { 1 } { 3 }$ 
B) -3, 5 
C)  $- \frac { 1 } { 3 } , \frac { 1 } { 5 }$ 
D) -5 , 3 
A)  $- \frac { 1 } { 5 } , \frac { 1 } { 3 }$ 
B) -3, 5 
C)  $- \frac { 1 } { 3 } , \frac { 1 } { 5 }$ 
D) -5 , 3

Question 5

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - 7 x - 18$

Accepted Answer

A) (x - 2)(x + 1) 
B) prime 
C) (x + 2)(x - 9) 
D) (x - 2)(x - 9) 
A) (x - 2)(x + 1) 
B) prime 
C) (x + 2)(x - 9) 
D) (x - 2)(x - 9)

Question 6

Solve.
-An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation h = -16t2 + 48t + 160. When will the
Object hit the ground?

Accepted Answer

A) 160 sec 
B) -2 sec 
C) 2 sec 
D) 5 sec 
A) 160 sec 
B) -2 sec 
C) 2 sec 
D) 5 sec

Question 7

Factor the binomial completely.
-$81 x ^ { 2 } - 25 y ^ { 2 }$

Accepted Answer

A)  $( 9 x + 5 y ) ^ { 2 }$ 
B) (9x + 5y)(9x - 5y) 
C)  $( 9 x - 5 y ) ^ { 2 }$ 
D) prime 
A)  $( 9 x + 5 y ) ^ { 2 }$ 
B) (9x + 5y)(9x - 5y) 
C)  $( 9 x - 5 y ) ^ { 2 }$ 
D) prime

Question 8

Solve the equation.
-3x(3x + 9)= 0

Accepted Answer

A) 0, 3 
B) 0, -3 
C) 0, -3 , 3 
D) 0, - 13 
A) 0, 3 
B) 0, -3 
C) 0, -3 , 3 
D) 0, - 13

Question 9

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

Accepted Answer

A) 7, -6 
B) 7, 6 
C) 7, -7, 6, -6 
D) -7, 6 
A) 7, -6 
B) 7, 6 
C) 7, -7, 6, -6 
D) -7, 6

Question 10

Solve.
-Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Accepted Answer

A) 17 m 
B) 10 m 
C) 18 m 
D) 9 m 
A) 17 m 
B) 10 m 
C) 18 m 
D) 9 m

Question 11

Factor the binomial completely.
-$25 a ^ { 3 } - 49 a$

Accepted Answer

A) a(5a + 7)(5a - 7) 
B)  $a ( 5 a - 7 ) ^ { 2 }$ 
C) a(25a + 1)(a - 49) 
D)  $\left( 5 a ^ { 2 } + 7 \right) ( 5 a - 7 )$ 
A) a(5a + 7)(5a - 7) 
B)  $a ( 5 a - 7 ) ^ { 2 }$ 
C) a(25a + 1)(a - 49) 
D)  $\left( 5 a ^ { 2 } + 7 \right) ( 5 a - 7 )$

Question 12

Solve the equation.
-$x ^ { 3 } = 3 x ^ { 2 } + 18 x$

Accepted Answer

A) -3, 6 
B) 0, -3, 6 
C) 3, -6 
D) 0, 3, -6 
A) -3, 6 
B) 0, -3, 6 
C) 3, -6 
D) 0, 3, -6

Question 13

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } - x - 20$

Accepted Answer

A) (x + 1)(x - 20) 
B) (x + 5)(x - 4) 
C) (x + 4)(x - 5) 
D) prime 
A) (x + 1)(x - 20) 
B) (x + 5)(x - 4) 
C) (x + 4)(x - 5) 
D) prime

Question 14

Factor the trinomial completely.
- $- 40 x ^ { 3 } - 84 x ^ { 2 } - 36 x$

Accepted Answer

A) x(-8x - 12)(5x + 3) 
B) -4x(2x + 3)(5x + 3) 
C) x(2x + 3)(-20x - 12) 
D) -4(2x2 + 3)(5x + 3) 
A) x(-8x - 12)(5x + 3) 
B) -4x(2x + 3)(5x + 3) 
C) x(2x + 3)(-20x - 12) 
D) -4(2x2 + 3)(5x + 3)

Question 15

Solve the equation.
-$\left( 2 x + \frac { 1 } { 5 } \right) \left( 4 x - \frac { 6 } { 7 } \right) = 0$

Accepted Answer

A)  $- \frac { 1 } { 5 } , \frac { 6 } { 7 }$ 
B)   $- \frac { 1 } { 10 } , \frac { 3 } { 7 }$ 
C)  $- \frac { 1 } { 5 } , \frac { 3 } { 14 }$ 
D)   $- \frac { 1 } { 10 } , \frac { 3 } { 14 }$ 
A)  $- \frac { 1 } { 5 } , \frac { 6 } { 7 }$ 
B)   $- \frac { 1 } { 10 } , \frac { 3 } { 7 }$ 
C)  $- \frac { 1 } { 5 } , \frac { 3 } { 14 }$ 
D)   $- \frac { 1 } { 10 } , \frac { 3 } { 14 }$

Question 16

Factor the trinomial completely.
-$6 x ^ { 2 } y ^ { 2 } - 5 x y ^ { 2 } - 25 y ^ { 2 }$

Accepted Answer

A) (3x - 5y)(2x + 5y) 
B) y2(x - 5)(6x + 5) 
C)  $y ^ { 2 } ( 2 x - 5 ) ( 3 x + 5 )$ 
D) (2x - 5y)(3x + 5y) 
A) (3x - 5y)(2x + 5y) 
B) y2(x - 5)(6x + 5) 
C)  $y ^ { 2 } ( 2 x - 5 ) ( 3 x + 5 )$ 
D) (2x - 5y)(3x + 5y)

Question 17

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 160 square centimeters. Find the side of the
Square.

Accepted Answer

A) 10 cm 
B) 64 cm 
C) 8 cm 
D) 2 cm 
A) 10 cm 
B) 64 cm 
C) 8 cm 
D) 2 cm

Question 18

Solve the equation.
-$4 ( x + 6 ) = - 4 x + 4 \left( x ^ { 2 } + 3 \right)$

Accepted Answer

A) 4, -1, -3 
B) 4, 1, 3 
C) 1, -3 
D) -1, 3 
A) 4, -1, -3 
B) 4, 1, 3 
C) 1, -3 
D) -1, 3

Question 19

Factor the trinomial completely.
-$3 x ^ { 2 } + 19 x + 20$

Accepted Answer

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

Question 20

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x y ^ { 2 } + 6 y ^ { 2 } - 9 x - 54$

Accepted Answer

A)  $( x + 6 ) ( y - 3 ) ^ { 2 }$ 
B) (x + 6)(y + 3)(y - 3) 
C)  $( x + 6 ) \left( y ^ { 2 } - 9 \right)$ 
D) (x - 6)(y + 3)(y - 3) 
A)  $( x + 6 ) ( y - 3 ) ^ { 2 }$ 
B) (x + 6)(y + 3)(y - 3) 
C)  $( x + 6 ) \left( y ^ { 2 } - 9 \right)$ 
D) (x - 6)(y + 3)(y - 3)

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $5 x ^ { 2 } y + 5 x y - 25 y$

Solve the equation. - $y ^ { 3 } + 10 y ^ { 2 } + 25 y = 0$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $y ^ { 2 } - 2 y - 80$

Solve the equation. -(x - 3)(3x + 15)= 0

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - 7 x - 18$

Solve. -An object is thrown upward from the top of a 160-foot building with an initial velocity of 48 feet per second. The height h of the object after t seconds is given by the quadratic equation h = -16t2 + 48t + 160. When will the Object hit the ground?

Factor the binomial completely. - $81 x ^ { 2 } - 25 y ^ { 2 }$

Solve the equation. -3x(3x + 9)= 0

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

Solve. -Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Factor the binomial completely. - $25 a ^ { 3 } - 49 a$

Solve the equation. - $x ^ { 3 } = 3 x ^ { 2 } + 18 x$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } - x - 20$

Factor the trinomial completely. - $- 40 x ^ { 3 } - 84 x ^ { 2 } - 36 x$

Solve the equation. - $\left( 2 x + \frac { 1 } { 5 } \right) \left( 4 x - \frac { 6 } { 7 } \right) = 0$

Factor the trinomial completely. - $6 x ^ { 2 } y ^ { 2 } - 5 x y ^ { 2 } - 25 y ^ { 2 }$

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 160 square centimeters. Find the side of the Square.

Solve the equation. - $4 ( x + 6 ) = - 4 x + 4 \left( x ^ { 2 } + 3 \right)$

Factor the trinomial completely. - $3 x ^ { 2 } + 19 x + 20$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x y ^ { 2 } + 6 y ^ { 2 } - 9 x - 54$

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Exam 13: Factoring Polynomials

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 5x2y+5xy−25y5 x ^ { 2 } y + 5 x y - 25 y5x2y+5xy−25y

Solve the equation. - y3+10y2+25y=0y ^ { 3 } + 10 y ^ { 2 } + 25 y = 0y3+10y2+25y=0

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - y2−2y−80y ^ { 2 } - 2 y - 80y2−2y−80