Question 1

Factor the trinomial completely.
-$x ^ { 2 } - 6 x + 36$

Accepted Answer

A)  $( x + 6 ) ^ { 2 }$ 
B)  $( x - 6 ) ^ { 2 }$ 
C) (x + 6)(x - 6) 
D) prime 
A)  $( x + 6 ) ^ { 2 }$ 
B)  $( x - 6 ) ^ { 2 }$ 
C) (x + 6)(x - 6) 
D) prime

Question 2

Solve the equation.
-$4 t ^ { 3 } - 81 t = 0$

Accepted Answer

A)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 }$ 
B)  $\frac { 9 } { 2 }$ 
C) 0 
D)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 } , 0$ 
A)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 }$ 
B)  $\frac { 9 } { 2 }$ 
C) 0 
D)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 } , 0$

Question 3

Solve.
-The width of a rectangle is 6 kilometers less than twice its length. If its area is 56 square kilometers, find the dimensions of the rectangle.

Accepted Answer

A) length = 4 km, width = 2 km 
B) length = 7 km, width = 8 km 
C) width = 7 km, length = 8 km 
D) length = 3 km, width = $\frac { 56 } { 3 }$ k km 
A) length = 4 km, width = 2 km 
B) length = 7 km, width = 8 km 
C) width = 7 km, length = 8 km 
D) length = 3 km, width = $\frac { 56 } { 3 }$ k km

Question 4

Solve the equation.
-  $- 40 x ^ { 2 } + 8 x = - 8 x ^ { 2 } - 4 x$

Accepted Answer

A)  $4 , \frac { 3 } { 8 }$ 
B)  $- 4 , - \frac { 3 } { 8 }$ 
C)  $0 , \frac { 3 } { 8 }$ 
D)   $0 , - \frac { 3 } { 8 }$ 
A)  $4 , \frac { 3 } { 8 }$ 
B)  $- 4 , - \frac { 3 } { 8 }$ 
C)  $0 , \frac { 3 } { 8 }$ 
D)   $0 , - \frac { 3 } { 8 }$

Question 5

Factor the polynomial by grouping.
-$3 x ^ { 3 } + 17 x ^ { 2 } + 10 x$

Accepted Answer

A) 3x(x + 5)(x + 2) 
B) x(3x + 5)(x + 2) 
C) x(x + 5)(3x + 2) 
D) prime 
A) 3x(x + 5)(x + 2) 
B) x(3x + 5)(x + 2) 
C) x(x + 5)(3x + 2) 
D) prime

Question 6

Find the GCF for the list.
-2x, x

Accepted Answer

A) 1 
B) 2 
C) x 
D) 2x 
A) 1 
B) 2 
C) x 
D) 2x

Question 7

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$4 x ^ { 3 } - 44 x ^ { 2 } + 120 x$

Accepted Answer

A) 4x(x + 5)(x + 6) 
B) x(4x + 5)(x + 6) 
C) x(x + 5)(4x + 24) 
D) 4x(x - 5)(x - 6) 
A) 4x(x + 5)(x + 6) 
B) x(4x + 5)(x + 6) 
C) x(x + 5)(4x + 24) 
D) 4x(x - 5)(x - 6)

Question 8

Factor the binomial completely.
-$64 - w ^ { 2 }$

Accepted Answer

A) (8 - w)(8 + w) 
B)  $( 8 - w ) ^ { 2 }$ 
C) ( $( 8 + w ) ^ { 2 }$ 
D) prime 
A) (8 - w)(8 + w) 
B)  $( 8 - w ) ^ { 2 }$ 
C) ( $( 8 + w ) ^ { 2 }$ 
D) prime

Question 9

The equationn   $D = \frac { 1 } { 2 } n ( n - 3 )$ gives the n gives the umber of diagonals D for a polygon with n sides. Use this equation to solve the problem.
-Find the number of diagonals for a polygon that has 14 sides.

Accepted Answer

A) 11 diagonals 
B) 77 diagonals 
C) 119 diagonals 
D) 154 diagonals 
A) 11 diagonals 
B) 77 diagonals 
C) 119 diagonals 
D) 154 diagonals

Question 10

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$2 x ^ { 3 } y ^ { 3 } - 4 x ^ { 3 } y ^ { 2 } - 30 x ^ { 3 } y$

Accepted Answer

A)  $2 x ^ { 3 } y ( y - 3 ) ( y + 5 )$ 
B)  $2 x ^ { 3 } y ( y + 3 ) ( y - 5 )$ 
C)  $x ^ { 3 } \left( 2 y ^ { 2 } + 6 y \right) ( y - 5 )$ 
D) prime 
A)  $2 x ^ { 3 } y ( y - 3 ) ( y + 5 )$ 
B)  $2 x ^ { 3 } y ( y + 3 ) ( y - 5 )$ 
C)  $x ^ { 3 } \left( 2 y ^ { 2 } + 6 y \right) ( y - 5 )$ 
D) prime

Question 11

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 12 x y + 32 y ^ { 2 }$

Accepted Answer

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

Question 12

Solve the equation.
-$x ^ { 2 } - 80 x - 81 = 0$

Accepted Answer

A) -1, 81 
B) 1, -81 
C) -9, 9 
D) -9, -9 
A) -1, 81 
B) 1, -81 
C) -9, 9 
D) -9, -9

Question 13

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$2 t ^ { 5 } - 2 t ^ { 4 } - 24 t ^ { 3 }$

Accepted Answer

A)  $2 t ^ { 3 } ( t - 3 ) ( t + 4 )$ 
B)  $2 t ^ { 3 } ( t + 3 ) ( t - 4 )$ 
C)  $\left( 2 t ^ { 4 } + 6 \right) ( t - 4 )$ 
D)  $( t - 3 ) ( 2 t + 48 )$ 
A)  $2 t ^ { 3 } ( t - 3 ) ( t + 4 )$ 
B)  $2 t ^ { 3 } ( t + 3 ) ( t - 4 )$ 
C)  $\left( 2 t ^ { 4 } + 6 \right) ( t - 4 )$ 
D)  $( t - 3 ) ( 2 t + 48 )$

Factor the trinomial completely. - $x ^ { 2 } - 6 x + 36$

Solve the equation. - $4 t ^ { 3 } - 81 t = 0$

Solve. -The width of a rectangle is 6 kilometers less than twice its length. If its area is 56 square kilometers, find the dimensions of the rectangle.

Solve the equation. - $- 40 x ^ { 2 } + 8 x = - 8 x ^ { 2 } - 4 x$

Factor the polynomial by grouping. - $3 x ^ { 3 } + 17 x ^ { 2 } + 10 x$

Find the GCF for the list. -2x, x

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $4 x ^ { 3 } - 44 x ^ { 2 } + 120 x$

Factor the binomial completely. - $64 - w ^ { 2 }$

The equationn $D = \frac { 1 } { 2 } n ( n - 3 )$ gives the n gives the umber of diagonals D for a polygon with n sides. Use this equation to solve the problem. -Find the number of diagonals for a polygon that has 14 sides.

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 3 } y ^ { 3 } - 4 x ^ { 3 } y ^ { 2 } - 30 x ^ { 3 } y$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 12 x y + 32 y ^ { 2 }$

Solve the equation. - $x ^ { 2 } - 80 x - 81 = 0$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $2 t ^ { 5 } - 2 t ^ { 4 } - 24 t ^ { 3 }$

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Exam 13: Factoring Polynomials

Factor the trinomial completely. - x2−6x+36x ^ { 2 } - 6 x + 36x2−6x+36

Solve the equation. - 4t3−81t=04 t ^ { 3 } - 81 t = 04t3−81t=0