Question 1

Complete the factored form.
-$20 x ^ { 2 } - 31 x + 12 = ( 5 x - 4 )$

Accepted Answer

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

Question 2

Find the x-intercepts of the graph of each equation.
-$y = x ^ { 2 } - 11 x + 30$

Accepted Answer

A)  $( 5,0 ) , ( 6,0 )$ 
B)  $\left( \frac { 1 } { 5 } , 0 \right) , \left( \frac { 1 } { 6 } , 0 \right)$ 
C)  $( - 5,0 ) , ( - 6,0 )$ 
D)  $( 5,0 ) , ( - 6,0 )$ 
A)  $( 5,0 ) , ( 6,0 )$ 
B)  $\left( \frac { 1 } { 5 } , 0 \right) , \left( \frac { 1 } { 6 } , 0 \right)$ 
C)  $( - 5,0 ) , ( - 6,0 )$ 
D)  $( 5,0 ) , ( - 6,0 )$

Question 3

Factor the perfect square trinomial completely.
-$16 \mathrm { k } ^ { 3 } \mathrm {~m} + 56 \mathrm { k } ^ { 2 } \mathrm {~m} ^ { 2 } + 49 \mathrm {~km} ^ { 3 }$

Accepted Answer

A)  $\mathrm { km } ( 4 \mathrm { k } + 7 \mathrm {~m} ) ( 4 \mathrm { k } - 7 \mathrm {~m} )$ 
B)  $\mathrm { km } ( 4 \mathrm { k } - 7 \mathrm {~m} ) ^ { 2 }$ 
C)  $\left( 16 \mathrm { k } ^ { 2 } \mathrm {~m} + \mathrm { km } \right) \left( \mathrm { k } + 49 \mathrm {~m} ^ { 2 } \right)$ 
D)  $k \mathrm {~m} ( 4 \mathrm { k } + 7 \mathrm {~m} ) ^ { 2 }$ 
A)  $\mathrm { km } ( 4 \mathrm { k } + 7 \mathrm {~m} ) ( 4 \mathrm { k } - 7 \mathrm {~m} )$ 
B)  $\mathrm { km } ( 4 \mathrm { k } - 7 \mathrm {~m} ) ^ { 2 }$ 
C)  $\left( 16 \mathrm { k } ^ { 2 } \mathrm {~m} + \mathrm { km } \right) \left( \mathrm { k } + 49 \mathrm {~m} ^ { 2 } \right)$ 
D)  $k \mathrm {~m} ( 4 \mathrm { k } + 7 \mathrm {~m} ) ^ { 2 }$

Question 4

Solve the equation.
-$\left( 2 x + \frac { 4 } { 5 } \right) \left( 4 x - \frac { 3 } { 7 } \right) = 0$

Accepted Answer

A)  $- \frac { 2 } { 5 } , \frac { 3 } { 28 }$ 
B)  $- \frac { 4 } { 5 } , \frac { 3 } { 7 }$ 
C)  $- \frac { 2 } { 5 } , \frac { 3 } { 14 }$ 
D)  $- \frac { 4 } { 5 } , \frac { 3 } { 28 }$ 
A)  $- \frac { 2 } { 5 } , \frac { 3 } { 28 }$ 
B)  $- \frac { 4 } { 5 } , \frac { 3 } { 7 }$ 
C)  $- \frac { 2 } { 5 } , \frac { 3 } { 14 }$ 
D)  $- \frac { 4 } { 5 } , \frac { 3 } { 28 }$

Question 5

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 $h = - 16 t ^ { 2 } + 48 t + 160$. When will the object hit the ground?

Accepted Answer

A)  $160 \mathrm { sec }$ 
B)  $2 \mathrm { sec }$ 
C)  $5 \mathrm { sec }$ 
D)  $- 2 \mathrm { sec }$ 
A)  $160 \mathrm { sec }$ 
B)  $2 \mathrm { sec }$ 
C)  $5 \mathrm { sec }$ 
D)  $- 2 \mathrm { sec }$

Question 6

Solve the equation.
-$7 x ( 8 x - 3 ) = 0$

Accepted Answer

A)  $\frac { 3 } { 8 } , \frac { 1 } { 7 } , 0$ 
B)  $- \frac { 3 } { 8 } , 0$ 
C)  $\frac { 3 } { 8 } , 0$ 
D)  $\frac { 3 } { 8 } , \frac { 1 } { 7 }$ 
A)  $\frac { 3 } { 8 } , \frac { 1 } { 7 } , 0$ 
B)  $- \frac { 3 } { 8 } , 0$ 
C)  $\frac { 3 } { 8 } , 0$ 
D)  $\frac { 3 } { 8 } , \frac { 1 } { 7 }$

Question 7

Solve.
-A triangular piece of glass is being cut so that the height of the triangle is 4 inches shorter than twice the base. If the area of the triangle is 288 square inches, how long is the height of the triangle?

Accepted Answer

A)  $36 \mathrm { in }$. 
B)  $34 \mathrm { in }$. 
C)  $32 \mathrm { in }$. 
D)  $18 \mathrm { in }$. 
A)  $36 \mathrm { in }$. 
B)  $34 \mathrm { in }$. 
C)  $32 \mathrm { in }$. 
D)  $18 \mathrm { in }$.

Question 8

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be
used more than once. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-The expression $a ^ { 3 } + b ^ { 3 }$ is called $a$________

Accepted Answer

A)  sum of two cubes 
B)  difference of two cubes 
C)  perfect square trinomial 
D)  difference of two squares 
A)  sum of two cubes 
B)  difference of two cubes 
C)  perfect square trinomial 
D)  difference of two squares

Question 9

Find a positive value of the given variable so that the trinomial is factorable.
-$\mathrm { y } ^ { 2 } + 2 \mathrm { y } + \mathrm { c } ; \mathrm { c } = \text { ? }$

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  1 
A)  2 
B)  3 
C)  4 
D)  1

Question 10

Factor the sum or difference of two cubes.
-$343 y ^ { 3 } - 512$

Accepted Answer

A)  $( 7 y - 8 ) \left( 49 y ^ { 2 } + 56 y + 64 \right)$ 
B)  $( 7 y - 8 ) \left( 49 y ^ { 2 } + 64 \right)$ 
C)  $( 7 y + 8 ) \left( 49 y ^ { 2 } - 56 y + 64 \right)$ 
D)  $( 343 y - 8 ) \left( y ^ { 2 } + 56 y + 64 \right)$ 
A)  $( 7 y - 8 ) \left( 49 y ^ { 2 } + 56 y + 64 \right)$ 
B)  $( 7 y - 8 ) \left( 49 y ^ { 2 } + 64 \right)$ 
C)  $( 7 y + 8 ) \left( 49 y ^ { 2 } - 56 y + 64 \right)$ 
D)  $( 343 y - 8 ) \left( y ^ { 2 } + 56 y + 64 \right)$

Question 11

Factor completely.
-$10 y ^ { 2 } - 23 y + 12$

Accepted Answer

A)  prime 
B)  $( 2 y - 3 ) ( 5 y - 4 )$ 
C)  $( 2 y + 3 ) ( 5 y + 4 )$ 
D)  $( 10 y + 3 ) ( y + 4 )$ 
A)  prime 
B)  $( 2 y - 3 ) ( 5 y - 4 )$ 
C)  $( 2 y + 3 ) ( 5 y + 4 )$ 
D)  $( 10 y + 3 ) ( y + 4 )$

Question 12

Solve.
-The equation $D = \frac { 1 } { 2 } n ( n - 3 )$ gives the number of diagonals $D$ for a polygon with $n$ sides. Find the number of sides $\mathrm { n }$ for a polygon that has 54 diagonals.

Accepted Answer

A)  9 sides 
B)  12 sides 
C)  3 sides 
D)  13 sides 
A)  9 sides 
B)  12 sides 
C)  3 sides 
D)  13 sides

Question 13

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$- y z ^ { 7 } - y ^ { 7 } z$

Accepted Answer

A)  $- y z ( y - z ) \left( y ^ { 6 } + y z + z ^ { 6 } \right)$ 
B)  $- y z ( y - z ) ( y - z )$ 
C)  $- y z \left( y ^ { 6 } + z ^ { 6 } \right)$ 
D)  $- y z ( y + z ) \left( y ^ { 6 } - y z + z ^ { 6 } \right)$ 
A)  $- y z ( y - z ) \left( y ^ { 6 } + y z + z ^ { 6 } \right)$ 
B)  $- y z ( y - z ) ( y - z )$ 
C)  $- y z \left( y ^ { 6 } + z ^ { 6 } \right)$ 
D)  $- y z ( y + z ) \left( y ^ { 6 } - y z + z ^ { 6 } \right)$

Question 14

Factor out the GCF from the polynomial.
-$40 x + 10$

Accepted Answer

A)  $10 ( 4 x )$ 
B)  $2 ( 20 x + 5 )$ 
C)  $10 ( 4 x + 1 )$ 
D)  $5 ( 8 x + 2 )$ 
A)  $10 ( 4 x )$ 
B)  $2 ( 20 x + 5 )$ 
C)  $10 ( 4 x + 1 )$ 
D)  $5 ( 8 x + 2 )$

Question 15

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$2 x ^ { 6 } - 14 x ^ { 5 } + 20 x ^ { 4 }$

Accepted Answer

A)  $x ^ { 4 } ( x - 5 ) ( 2 x - 4 )$ 
B)  $2 x ^ { 4 } \left( x ^ { 2 } - 7 x + 10 \right)$ 
C)  $x ^ { 4 } ( 2 x - 10 ) ( x - 2 )$ 
D)  $2 x ^ { 4 } ( x - 5 ) ( x - 2 )$ 
A)  $x ^ { 4 } ( x - 5 ) ( 2 x - 4 )$ 
B)  $2 x ^ { 4 } \left( x ^ { 2 } - 7 x + 10 \right)$ 
C)  $x ^ { 4 } ( 2 x - 10 ) ( x - 2 )$ 
D)  $2 x ^ { 4 } ( x - 5 ) ( x - 2 )$

Question 16

Factor the binomial completely.
-$49 y ^ { 2 } - ( x + 3 ) ^ { 2 }$

Accepted Answer

A)  $( 7 y + 3 x ) ( 7 y - 3 x )$ 
B)  $( 7 y + x + 3 ) ( 7 y - x + 3 )$ 
C)  $( 7 y - x - 3 ) ^ { 2 }$ 
D)  $( 7 y + x + 3 ) ( 7 y - x - 3 )$ 
A)  $( 7 y + 3 x ) ( 7 y - 3 x )$ 
B)  $( 7 y + x + 3 ) ( 7 y - x + 3 )$ 
C)  $( 7 y - x - 3 ) ^ { 2 }$ 
D)  $( 7 y + x + 3 ) ( 7 y - x - 3 )$

Question 17

Solve the equation.
-$x ^ { 2 } + 3 x = 40$

Accepted Answer

A)  $- 8,1$ 
B)  $8 , - 5$ 
C)  $- 8,5$ 
D)  8,5 
A)  $- 8,1$ 
B)  $8 , - 5$ 
C)  $- 8,5$ 
D)  8,5

Question 18

Find the x-intercepts of the graph of each equation.
-$y = 5 x ^ { 2 } - 19 x - 4$

Accepted Answer

A)  $\left( - \frac { 1 } { 5 } , 0 \right) , ( 4,0 )$ 
B)  $( - 5,0 ) , ( 4,0 )$ 
C)  $\left( \frac { 1 } { 19 } , 0 \right) , \left( - \frac { 1 } { 5 } , 0 \right)$ 
D)  $\left( - \frac { 1 } { 5 } , 0 \right)$, 
A)  $\left( - \frac { 1 } { 5 } , 0 \right) , ( 4,0 )$ 
B)  $( - 5,0 ) , ( 4,0 )$ 
C)  $\left( \frac { 1 } { 19 } , 0 \right) , \left( - \frac { 1 } { 5 } , 0 \right)$ 
D)  $\left( - \frac { 1 } { 5 } , 0 \right)$,

Question 19

Factor the binomial completely.
-$z ^ { 2 } - 16$

Accepted Answer

A)  $( z + 4 ) ( z - 4 )$ 
B)  $( \mathrm { z } + 4 ) ^ { 2 }$ 
C)  prime 
D)  $( z - 4 ) ^ { 2 }$ 
A)  $( z + 4 ) ( z - 4 )$ 
B)  $( \mathrm { z } + 4 ) ^ { 2 }$ 
C)  prime 
D)  $( z - 4 ) ^ { 2 }$

Question 20

Fill in the blank with one of the words or phrases listed below. Not all choices will be used and some choices may be
used more than once. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-________is the process of writing an expression as a product.

Accepted Answer

A)  Quadratic Equation 
B)  Perfect Square trinomial 
C)  Factoring 
D)  Greatest common factor 
A)  Quadratic Equation 
B)  Perfect Square trinomial 
C)  Factoring 
D)  Greatest common factor

Complete the factored form. - $20 x ^ { 2 } - 31 x + 12 = ( 5 x - 4 )$

Find the x-intercepts of the graph of each equation. - $y = x ^ { 2 } - 11 x + 30$

Factor the perfect square trinomial completely. - $16 \mathrm { k } ^ { 3 } \mathrm {~m} + 56 \mathrm { k } ^ { 2 } \mathrm {~m} ^ { 2 } + 49 \mathrm {~km} ^ { 3 }$

Solve the equation. - $\left( 2 x + \frac { 4 } { 5 } \right) \left( 4 x - \frac { 3 } { 7 } \right) = 0$

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 $h = - 16 t ^ { 2 } + 48 t + 160$ . When will the object hit the ground?

Solve the equation. - $7 x ( 8 x - 3 ) = 0$

Solve. -A triangular piece of glass is being cut so that the height of the triangle is 4 inches shorter than twice the base. If the area of the triangle is 288 square inches, how long is the height of the triangle?

Find a positive value of the given variable so that the trinomial is factorable. - $\mathrm { y } ^ { 2 } + 2 \mathrm { y } + \mathrm { c } ; \mathrm { c } = \text { ? }$

Factor the sum or difference of two cubes. - $343 y ^ { 3 } - 512$

Factor completely. - $10 y ^ { 2 } - 23 y + 12$

Solve. -The equation $D = \frac { 1 } { 2 } n ( n - 3 )$ gives the number of diagonals $D$ for a polygon with $n$ sides. Find the number of sides $\mathrm { n }$ for a polygon that has 54 diagonals.

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $- y z ^ { 7 } - y ^ { 7 } z$

Factor out the GCF from the polynomial. - $40 x + 10$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $2 x ^ { 6 } - 14 x ^ { 5 } + 20 x ^ { 4 }$

Factor the binomial completely. - $49 y ^ { 2 } - ( x + 3 ) ^ { 2 }$

Solve the equation. - $x ^ { 2 } + 3 x = 40$

Find the x-intercepts of the graph of each equation. - $y = 5 x ^ { 2 } - 19 x - 4$

Factor the binomial completely. - $z ^ { 2 } - 16$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring Polynomials

Complete the factored form. - 20x2−31x+12=(5x−4)20 x ^ { 2 } - 31 x + 12 = ( 5 x - 4 )20x2−31x+12=(5x−4)

Find the x-intercepts of the graph of each equation. - y=x2−11x+30y = x ^ { 2 } - 11 x + 30y=x2−11x+30

Factor the perfect square trinomial completely. - 16k3 m+56k2 m2+49 km316 \mathrm { k } ^ { 3 } \mathrm {~m} + 56 \mathrm { k } ^ { 2 } \mathrm {~m} ^ { 2 } + 49 \mathrm {~km} ^ { 3 }16k3 m+56k2 m2+49 km3

Solve the equation. - (2x+45)(4x−37)=0\left( 2 x + \frac { 4 } { 5 } \right) \left( 4 x - \frac { 3 } { 7 } \right) = 0(2x+54​)(4x−73​)=0

Solve the equation. - 7x(8x−3)=07 x ( 8 x - 3 ) = 07x(8x−3)=0