Question 1

Solve.
-The sum of two numbers is 14, and the sum of their squares is 100. Find the numbers.

Accepted Answer

A)  10 and 4 
B)  8 and 6 
C)  9 and 5 
D)  7 and 7 
A)  10 and 4 
B)  8 and 6 
C)  9 and 5 
D)  7 and 7 B

Question 2

Complete the factored form.
-$5 x ^ { 2 } + 13 x - 6 = ( 5 x - 2 )$

Accepted Answer

A)  $( 5 x + 2 )$ 
B)  $( x + 3 )$ 
C)  $( 5 x - 3 )$ 
D)  $( x - 3 )$ 
A)  $( 5 x + 2 )$ 
B)  $( x + 3 )$ 
C)  $( 5 x - 3 )$ 
D)  $( x - 3 )$ B

Question 3

Solve the equation.
-$64 x ^ { 3 } - x = 0$

Accepted Answer

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

Question 4

Factor the four-term polynomial by grouping.
-$3 y - 18 + x y - 6 x$

Accepted Answer

A)  $( y - 6 x ) ( 3 + x )$ 
B)  $( x - 6 ) ( y + 3 )$ 
C)  $( y - 6 ) ( 3 + x )$ 
D)  $( x - 6 ) ( 3 y + x )$ 
A)  $( y - 6 x ) ( 3 + x )$ 
B)  $( x - 6 ) ( y + 3 )$ 
C)  $( y - 6 ) ( 3 + x )$ 
D)  $( x - 6 ) ( 3 y + x )$

Question 5

Factor the four-term polynomial by grouping.
-$12 x ^ { 6 } - 9 x ^ { 3 } + 8 x ^ { 3 } - 6$

Accepted Answer

A)  $\left( 3 x ^ { 3 } + 2 \right) \left( 4 x ^ { 3 } - 3 \right)$ 
B)  $\left( 3 x ^ { 6 } + 2 \right) ( 4 x - 3 )$ 
C)  $\left( 3 x ^ { 3 } - 2 \right) \left( 4 x ^ { 3 } + 3 \right)$ 
D)  $\left( 12 x ^ { 3 } - 2 \right) \left( x ^ { 3 } + 3 \right)$ 
A)  $\left( 3 x ^ { 3 } + 2 \right) \left( 4 x ^ { 3 } - 3 \right)$ 
B)  $\left( 3 x ^ { 6 } + 2 \right) ( 4 x - 3 )$ 
C)  $\left( 3 x ^ { 3 } - 2 \right) \left( 4 x ^ { 3 } + 3 \right)$ 
D)  $\left( 12 x ^ { 3 } - 2 \right) \left( x ^ { 3 } + 3 \right)$

Question 6

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$x y ^ { 2 } + 2 y ^ { 2 } - 9 x - 18$

Accepted Answer

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

Question 7

Factor out the GCF from the polynomial.
-$14 x ^ { 3 } - 4 x ^ { 2 } + 8 x$

Accepted Answer

A)  $2 x \left( 7 x ^ { 2 } - 2 x + 4 \right)$ 
B)  $2 x \left( 7 x ^ { 3 } - 2 x ^ { 2 } + 4 x \right)$ 
C)  $2 \left( 7 x ^ { 3 } - 2 x ^ { 2 } + 4 x \right)$ 
D)  $x \left( 14 x ^ { 2 } - 4 x + 8 \right)$ 
A)  $2 x \left( 7 x ^ { 2 } - 2 x + 4 \right)$ 
B)  $2 x \left( 7 x ^ { 3 } - 2 x ^ { 2 } + 4 x \right)$ 
C)  $2 \left( 7 x ^ { 3 } - 2 x ^ { 2 } + 4 x \right)$ 
D)  $x \left( 14 x ^ { 2 } - 4 x + 8 \right)$

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. $$\begin{array} { l l l l } 
\text { factoring } & \text { quadratic equation } & \text { perfect square trinomial } & 0 \
\text { greatest common factor } & \text { hypotenuse } & \text { sum of two cubes } & 1 \
\text { difference of two cubes } & \text { difference of two squares } & \text { triangle } & \text { leg }
\end{array}$$
-A trinomial that is the square of some binomial is called a ________

Accepted Answer

A)  quadratic equation 
B)  perfect square trinomial 
C)  difference of two squares 
D)  greatest common factor 
A)  quadratic equation 
B)  perfect square trinomial 
C)  difference of two squares 
D)  greatest common factor

Question 9

Factor the four-term polynomial by grouping.
-$x ^ { 3 } + 7 x + x ^ { 2 } + 7$

Accepted Answer

A)  $\left( x ^ { 2 } + 7 \right) ( x + 1 )$ 
B)  $\left( x ^ { 2 } + 1 \right) ( 7 x + 1 )$ 
C)  $\left( x ^ { 2 } + 1 \right) ( x + 7 )$ 
D)  $( 7 x + 1 ) ( x + 1 )$ 
A)  $\left( x ^ { 2 } + 7 \right) ( x + 1 )$ 
B)  $\left( x ^ { 2 } + 1 \right) ( 7 x + 1 )$ 
C)  $\left( x ^ { 2 } + 1 \right) ( x + 7 )$ 
D)  $( 7 x + 1 ) ( x + 1 )$

Question 10

Factor the binomial completely.
-$\mathrm { r } ^ { 20 } - \mathrm { b } ^ { 2 }$

Accepted Answer

A)  $\left( \mathrm { r } ^ { 10 } + \mathrm { b } \right) \left( \mathrm { r } ^ { 10 } - \mathrm { b } \right)$ 
B)  prime 
C)  $\left( r ^ { 10 } - b \right) ^ { 2 }$ 
D)  $\left( \mathrm { r } ^ { 10 } + \mathrm { b } \right) ^ { 2 }$ 
A)  $\left( \mathrm { r } ^ { 10 } + \mathrm { b } \right) \left( \mathrm { r } ^ { 10 } - \mathrm { b } \right)$ 
B)  prime 
C)  $\left( r ^ { 10 } - b \right) ^ { 2 }$ 
D)  $\left( \mathrm { r } ^ { 10 } + \mathrm { b } \right) ^ { 2 }$

Question 11

Solve the equation.
-$\mathrm { t } ^ { 2 } + 8 \mathrm { t } - 33 = 0$

Accepted Answer

A)  $- 11,3$ 
B)  $11 , - 3$ 
C)  $- 11,1$ 
D)  11,3 
A)  $- 11,3$ 
B)  $11 , - 3$ 
C)  $- 11,1$ 
D)  11,3

Question 12

Solve the equation.
-$81 x ^ { 2 } - 25 = 0$

Accepted Answer

A)  $\frac { 5 } { 9 } , - \frac { 5 } { 9 } , 0$ 
B)  $\frac { 5 } { 9 } , - \frac { 5 } { 9 }$ 
C)  $\frac { 5 } { 9 }$ 
D)  $- \frac { 5 } { 9 }$ 
A)  $\frac { 5 } { 9 } , - \frac { 5 } { 9 } , 0$ 
B)  $\frac { 5 } { 9 } , - \frac { 5 } { 9 }$ 
C)  $\frac { 5 } { 9 }$ 
D)  $- \frac { 5 } { 9 }$

Question 13

Solve the equation.
-$x ^ { 2 } + 7 x = 18$

Accepted Answer

A)  9,2 
B)  $- 9,2$ 
C)  $9 , - 2$ 
D)  $- 9,1$ 
A)  9,2 
B)  $- 9,2$ 
C)  $9 , - 2$ 
D)  $- 9,1$

Question 14

Find the x-intercepts of the graph of each equation.
-$y = 21 x ^ { 2 } + 6 x$

Accepted Answer

A)  $\left( - \frac { 2 } { 7 } , 0 \right)$ 
B)  $( 0,0 )$ 
C)  $\left( - \frac { 2 } { 7 } , 0 \right) , ( 0,0 )$ 
D)  $\left( - \frac { 2 } { 7 } , 0 \right) , ( 6,0 )$ 
A)  $\left( - \frac { 2 } { 7 } , 0 \right)$ 
B)  $( 0,0 )$ 
C)  $\left( - \frac { 2 } { 7 } , 0 \right) , ( 0,0 )$ 
D)  $\left( - \frac { 2 } { 7 } , 0 \right) , ( 6,0 )$

Question 15

Factor out the GCF from the polynomial.
-$7 a ( a - b ) + ( a - b )$

Accepted Answer

A)  $7 a ( a - b )$ 
B)  $8 a ( a - b )$ 
C)  $\left( 7 a ^ { 2 } - 7 a b \right) + ( a - b )$ 
D)  $( a - b ) ( 7 a + 1 )$ 
A)  $7 a ( a - b )$ 
B)  $8 a ( a - b )$ 
C)  $\left( 7 a ^ { 2 } - 7 a b \right) + ( a - b )$ 
D)  $( a - b ) ( 7 a + 1 )$

Question 16

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 2 } + 3 x y - 18 y ^ { 2 }$

Accepted Answer

A)  $( x + 6 y ) ( x - 3 y )$ 
B)  $( x - 6 y ) ( x + y )$ 
C)  $( x - y ) ( x + 3 y )$ 
D)  $( x - 6 y ) ( x + 3 y )$ 
A)  $( x + 6 y ) ( x - 3 y )$ 
B)  $( x - 6 y ) ( x + y )$ 
C)  $( x - y ) ( x + 3 y )$ 
D)  $( x - 6 y ) ( x + 3 y )$

Question 17

Solve.
-A window washer accidentally drops a bucket from the top of a 144-foot building. The height $h$ of the bucket after $\mathrm { t }$ seconds is given by $\mathrm { h } = - 16 \mathrm { t } ^ { 2 } + 144$. When will the bucket hit the ground?

Accepted Answer

A)  $3 \mathrm { sec }$ 
B)  $9 \mathrm { sec }$ 
C)  $48 \mathrm { sec }$ 
D)  $- 3 \mathrm { sec }$ 
A)  $3 \mathrm { sec }$ 
B)  $9 \mathrm { sec }$ 
C)  $48 \mathrm { sec }$ 
D)  $- 3 \mathrm { sec }$

Question 18

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$3 t ^ { 5 } - 3 t ^ { 4 } - 18 t ^ { 3 }$

Accepted Answer

A)  $3 t ^ { 3 } ( t + 2 ) ( t - 3 )$ 
B)  $( t - 2 ) \left( 3 t ^ { 4 } + 9 \right)$ 
C)  $\left( 3 t ^ { 4 } + 6 \right) ( t - 3 )$ 
D)  $3 t ^ { 3 } ( t - 2 ) ( t + 3 )$ 
A)  $3 t ^ { 3 } ( t + 2 ) ( t - 3 )$ 
B)  $( t - 2 ) \left( 3 t ^ { 4 } + 9 \right)$ 
C)  $\left( 3 t ^ { 4 } + 6 \right) ( t - 3 )$ 
D)  $3 t ^ { 3 } ( t - 2 ) ( t + 3 )$

Question 19

Factor completely.
-$21 x ^ { 2 } - 91 x - 70$

Accepted Answer

A)  $7 ( 3 x + 2 ) ( x - 5 )$ 
B)  prime 
C)  $( 21 x + 14 ) ( x - 5 )$ 
D)  $7 ( 3 x - 2 ) ( x + 5 )$ 
A)  $7 ( 3 x + 2 ) ( x - 5 )$ 
B)  prime 
C)  $( 21 x + 14 ) ( x - 5 )$ 
D)  $7 ( 3 x - 2 ) ( x + 5 )$

Question 20

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$3 x ^ { 3 } + 6 x ^ { 2 } y - 45 x y ^ { 2 }$

Accepted Answer

A)  prime 
B)  $3 x ( x - 3 y ) ( x + 5 y )$ 
C)  $3 x ( x + 3 y ) ( x - 5 y )$ 
D)  $( x - 3 y ) \left( 3 x ^ { 2 } + 15 x y \right)$ 
A)  prime 
B)  $3 x ( x - 3 y ) ( x + 5 y )$ 
C)  $3 x ( x + 3 y ) ( x - 5 y )$ 
D)  $( x - 3 y ) \left( 3 x ^ { 2 } + 15 x y \right)$

Solve. -The sum of two numbers is 14, and the sum of their squares is 100. Find the numbers.

Complete the factored form. - $5 x ^ { 2 } + 13 x - 6 = ( 5 x - 2 )$

Solve the equation. - $64 x ^ { 3 } - x = 0$

Factor the four-term polynomial by grouping. - $3 y - 18 + x y - 6 x$

Factor the four-term polynomial by grouping. - $12 x ^ { 6 } - 9 x ^ { 3 } + 8 x ^ { 3 } - 6$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $x y ^ { 2 } + 2 y ^ { 2 } - 9 x - 18$

Factor out the GCF from the polynomial. - $14 x ^ { 3 } - 4 x ^ { 2 } + 8 x$

Factor the four-term polynomial by grouping. - $x ^ { 3 } + 7 x + x ^ { 2 } + 7$

Factor the binomial completely. - $\mathrm { r } ^ { 20 } - \mathrm { b } ^ { 2 }$

Solve the equation. - $\mathrm { t } ^ { 2 } + 8 \mathrm { t } - 33 = 0$

Solve the equation. - $81 x ^ { 2 } - 25 = 0$

Solve the equation. - $x ^ { 2 } + 7 x = 18$

Find the x-intercepts of the graph of each equation. - $y = 21 x ^ { 2 } + 6 x$

Factor out the GCF from the polynomial. - $7 a ( a - b ) + ( a - b )$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 2 } + 3 x y - 18 y ^ { 2 }$

Solve. -A window washer accidentally drops a bucket from the top of a 144-foot building. The height $h$ of the bucket after $\mathrm { t }$ seconds is given by $\mathrm { h } = - 16 \mathrm { t } ^ { 2 } + 144$ . When will the bucket hit the ground?

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $3 t ^ { 5 } - 3 t ^ { 4 } - 18 t ^ { 3 }$

Factor completely. - $21 x ^ { 2 } - 91 x - 70$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $3 x ^ { 3 } + 6 x ^ { 2 } y - 45 x y ^ { 2 }$

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

Solve. -The sum of two numbers is 14, and the sum of their squares is 100. Find the numbers.

Complete the factored form. - 5x2+13x−6=(5x−2)5 x ^ { 2 } + 13 x - 6 = ( 5 x - 2 )5x2+13x−6=(5x−2)

Solve the equation. - 64x3−x=064 x ^ { 3 } - x = 064x3−x=0

Factor the four-term polynomial by grouping. - 3y−18+xy−6x3 y - 18 + x y - 6 x3y−18+xy−6x

Factor the four-term polynomial by grouping. - 12x6−9x3+8x3−612 x ^ { 6 } - 9 x ^ { 3 } + 8 x ^ { 3 } - 612x6−9x3+8x3−6

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - xy2+2y2−9x−18x y ^ { 2 } + 2 y ^ { 2 } - 9 x - 18xy2+2y2−9x−18

Factor out the GCF from the polynomial. - 14x3−4x2+8x14 x ^ { 3 } - 4 x ^ { 2 } + 8 x14x3−4x2+8x

Factor the four-term polynomial by grouping. - x3+7x+x2+7x ^ { 3 } + 7 x + x ^ { 2 } + 7x3+7x+x2+7

Factor the binomial completely. - r20−b2\mathrm { r } ^ { 20 } - \mathrm { b } ^ { 2 }r20−b2

Solve the equation. - t2+8t−33=0\mathrm { t } ^ { 2 } + 8 \mathrm { t } - 33 = 0t2+8t−33=0

Solve the equation. - 81x2−25=081 x ^ { 2 } - 25 = 081x2−25=0

Solve the equation. - x2+7x=18x ^ { 2 } + 7 x = 18x2+7x=18

Find the x-intercepts of the graph of each equation. - y=21x2+6xy = 21 x ^ { 2 } + 6 xy=21x2+6x

Factor out the GCF from the polynomial. - 7a(a−b)+(a−b)7 a ( a - b ) + ( a - b )7a(a−b)+(a−b)

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x2+3xy−18y2x ^ { 2 } + 3 x y - 18 y ^ { 2 }x2+3xy−18y2

Solve. -A window washer accidentally drops a bucket from the top of a 144-foot building. The height hhh of the bucket after t\mathrm { t }t seconds is given by h=−16t2+144\mathrm { h } = - 16 \mathrm { t } ^ { 2 } + 144h=−16t2+144 . When will the bucket hit the ground?

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 3t5−3t4−18t33 t ^ { 5 } - 3 t ^ { 4 } - 18 t ^ { 3 }3t5−3t4−18t3

Factor completely. - 21x2−91x−7021 x ^ { 2 } - 91 x - 7021x2−91x−70

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - 3x3+6x2y−45xy23 x ^ { 3 } + 6 x ^ { 2 } y - 45 x y ^ { 2 }3x3+6x2y−45xy2