Question 1

Factor the GCF out of the given expression.
-$$4 t ^ { 2 } - 8 t - 8$$

Accepted Answer

A)  $4 t \left( t ^ { 2 } - 2 t - 2 \right)$ 
B)  $4 \left( t ^ { 2 } - 2 t - 2 \right)$ 
C)  $4 \left( t ^ { 2 } - 4 t - 4 \right)$ 
D)  $4 \left( t ^ { 2 } - 8 t - 8 \right)$ 
A)  $4 t \left( t ^ { 2 } - 2 t - 2 \right)$ 
B)  $4 \left( t ^ { 2 } - 2 t - 2 \right)$ 
C)  $4 \left( t ^ { 2 } - 4 t - 4 \right)$ 
D)  $4 \left( t ^ { 2 } - 8 t - 8 \right)$

Question 2

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-A triangle is 5 centimeters wider than it is tall. The area is 102 square cm. Find the width (length of the base).

Accepted Answer

A)  18 centimeters 
B)  5 centimeters 
C)  12 centimeters 
D)  17 centimeters 
A)  18 centimeters 
B)  5 centimeters 
C)  12 centimeters 
D)  17 centimeters

Question 3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$5 x ^ { 2 } + 13 x + 6$$

Accepted Answer

A)  $( x - 4 ) ( x + 2 )$ 
B)  $( x + 3 ) ( x + 2 )$ 
C)  $( 5 x - 4 ) ( x + 2 )$ 
D)  $( 5 x + 3 ) ( x + 2 )$ 
A)  $( x - 4 ) ( x + 2 )$ 
B)  $( x + 3 ) ( x + 2 )$ 
C)  $( 5 x - 4 ) ( x + 2 )$ 
D)  $( 5 x + 3 ) ( x + 2 )$

Question 4

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 4 } - s ^ { 4 }$$

Accepted Answer

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

Question 5

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-If a projectile is launched upward from a height of 32 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the function $h ( t ) = - 16 t ^ { 2 } + 64 t + 32$

Accepted Answer

A)  1 seconds 
B)  2 seconds 
C)  4 seconds 
D)  8 seconds 
A)  1 seconds 
B)  2 seconds 
C)  4 seconds 
D)  8 seconds

Question 6

Find the GCF.
-$64 a ^ { 8 } b ^ { 4 } , 56 a ^ { 6 } b ^ { 8 }$

Accepted Answer

A)  $448 a ^ { 8 } b ^ { 8 }$ 
B)  $8 a ^ { 6 } b ^ { 4 }$ 
C)  $4 a ^ { 2 } b ^ { 4 }$ 
D)  $8 a ^ { 8 } b ^ { 8 }$ 
A)  $448 a ^ { 8 } b ^ { 8 }$ 
B)  $8 a ^ { 6 } b ^ { 4 }$ 
C)  $4 a ^ { 2 } b ^ { 4 }$ 
D)  $8 a ^ { 8 } b ^ { 8 }$

Question 7

Factor by grouping.
-$$x ^ { 3 } - x ^ { 2 } + 9 x - 9$$

Accepted Answer

A)  $\left( x ^ { 2 } - 9 \right) ( x + 1 )$ 
B)  $\left( x ^ { 2 } + 9 \right) ( x - 1 )$ 
C)  $\left( x ^ { 2 } - 1 \right) ( x + 9 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( x - 9 )$ 
A)  $\left( x ^ { 2 } - 9 \right) ( x + 1 )$ 
B)  $\left( x ^ { 2 } + 9 \right) ( x - 1 )$ 
C)  $\left( x ^ { 2 } - 1 \right) ( x + 9 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( x - 9 )$

Question 8

Solve the problem.
-Let $f ( x ) = x ^ { 2 } - x - 56$. Find all values $x$ for which $f ( x ) = 0$.

Accepted Answer

A)  1,56 
B)  $- 7 , - 8$ 
C)  7,8 
D)  $- 7,8$ 
A)  1,56 
B)  $- 7 , - 8$ 
C)  7,8 
D)  $- 7,8$

Question 9

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$5 x ^ { 5 } + 20 x ^ { 4 } - 105 x ^ { 3 }$$

Accepted Answer

A)  $x ^ { 3 } ( 5 x - 15 ) ( x + 7 )$ 
B)  $5 x ^ { 3 } ( x - 3 ) ( x + 7 )$ 
C)  $5 x ^ { 3 } \left( x ^ { 2 } + 4 x - 21 \right)$ 
D)  $x ^ { 3 } ( x - 3 ) ( 5 x + 35 )$ 
A)  $x ^ { 3 } ( 5 x - 15 ) ( x + 7 )$ 
B)  $5 x ^ { 3 } ( x - 3 ) ( x + 7 )$ 
C)  $5 x ^ { 3 } \left( x ^ { 2 } + 4 x - 21 \right)$ 
D)  $x ^ { 3 } ( x - 3 ) ( 5 x + 35 )$

Question 10

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$3 x ^ { 2 } + 3 x - 18$$

Accepted Answer

A)  $3 x ( x + 2 y ) ( x - 3 y )$ 
B)  $3 ( x - 2 ) ( x + 3 )$ 
C)  $( 3 x + 6 x ) ( x - 3 )$ 
D)  Prime 
A)  $3 x ( x + 2 y ) ( x - 3 y )$ 
B)  $3 ( x - 2 ) ( x + 3 )$ 
C)  $( 3 x + 6 x ) ( x - 3 )$ 
D)  Prime

Question 11

Factor the GCF out of the given expression.
-$x ^ { 8 } - 9 x ^ { 3 }$

Accepted Answer

A)  $x ^ { 3 } \left( x ^ { 5 } + 9 \right)$ 
B)  $x ^ { 5 } \left( x ^ { 3 } - 9 \right)$ 
C)  $x \left( x ^ { 7 } - 9 x ^ { 2 } \right)$ 
D)  $x ^ { 3 } \left( x ^ { 5 } - 9 \right)$ 
A)  $x ^ { 3 } \left( x ^ { 5 } + 9 \right)$ 
B)  $x ^ { 5 } \left( x ^ { 3 } - 9 \right)$ 
C)  $x \left( x ^ { 7 } - 9 x ^ { 2 } \right)$ 
D)  $x ^ { 3 } \left( x ^ { 5 } - 9 \right)$

Question 12

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$25 x ^ { 2 } - 49$

Accepted Answer

A)  $( 5 x - 7 ) ^ { 2 }$ 
B)  $( 5 x + 7 ) ^ { 2 }$ 
C)  $( 25 x + 1 ) ( x - 49 )$ 
D)  $( 5 x + 7 ) ( 5 x - 7 )$ 
A)  $( 5 x - 7 ) ^ { 2 }$ 
B)  $( 5 x + 7 ) ^ { 2 }$ 
C)  $( 25 x + 1 ) ( x - 49 )$ 
D)  $( 5 x + 7 ) ( 5 x - 7 )$

Question 13

Find the GCF.
-30,36

Accepted Answer

A)  1 
B)  6 
C)  2 
D)  3 
A)  1 
B)  6 
C)  2 
D)  3

Question 14

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$8 x ^ { 2 } - 8$

Accepted Answer

A)  $8 ( x - 1 ) ( x + 1 )$ 
B)  $8 ( x + 1 ) ^ { 2 }$ 
C)  $( 8 x - 8 ) ( x + 1 )$ 
D)  $( 8 x - 1 ) ( x + 8 )$ 
A)  $8 ( x - 1 ) ( x + 1 )$ 
B)  $8 ( x + 1 ) ^ { 2 }$ 
C)  $( 8 x - 8 ) ( x + 1 )$ 
D)  $( 8 x - 1 ) ( x + 8 )$

Question 15

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-A rock falls from a tower that is 464 feet high. As it is falling, its height is given by the function $h ( t ) = - 16 t ^ { 2 } + 464 t$

Accepted Answer

A)  21.2 seconds 
B)  5.4 seconds 
C)  21.5 seconds 
D)  13,456 seconds 
A)  21.2 seconds 
B)  5.4 seconds 
C)  21.5 seconds 
D)  13,456 seconds

Question 16

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$3 x ^ { 8 } - 15 x ^ { 7 } + 12 x ^ { 6 }$$

Accepted Answer

A)  $3 ( x + 4 ) \left( x ^ { 7 } + 1 \right)$ 
B)  $3 x ^ { 6 } ( x - 4 ) ( x - 1 )$ 
C)  $x ^ { 6 } ( 3 x - 4 ) ( x + 1 )$ 
D)  $3 x ^ { 6 } ( x + 4 ) ( x - 1 )$ 
A)  $3 ( x + 4 ) \left( x ^ { 7 } + 1 \right)$ 
B)  $3 x ^ { 6 } ( x - 4 ) ( x - 1 )$ 
C)  $x ^ { 6 } ( 3 x - 4 ) ( x + 1 )$ 
D)  $3 x ^ { 6 } ( x + 4 ) ( x - 1 )$

Question 17

Find the missing value such that the given binomial is a factor of the given polynomial.
-$x ^ { 2 } - 18 x + ? , x - 9$

Accepted Answer

A)  $- 18$ 
B)  $- 9$ 
C)  81 
D)  1 
A)  $- 18$ 
B)  $- 9$ 
C)  81 
D)  1

Question 18

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$3 x ^ { 3 } - 12 x ^ { 2 } - 135 x$$

Accepted Answer

A)  $3 \left( x ^ { 2 } - 9 x \right) ( x + 5 )$ 
B)  $x ( x - 9 ) ( 3 x + 15 )$ 
C)  $3 x ( x - 9 ) ( x + 5 )$ 
D)  $x ( 3 x - 27 ) ( x + 5 )$ 
A)  $3 \left( x ^ { 2 } - 9 x \right) ( x + 5 )$ 
B)  $x ( x - 9 ) ( 3 x + 15 )$ 
C)  $3 x ( x - 9 ) ( x + 5 )$ 
D)  $x ( 3 x - 27 ) ( x + 5 )$

Question 19

Factor the GCF out of the given expression.
-$$3 x ( x + 5 ) + 2 ( x + 5 )$$

Accepted Answer

A)  $( 3 x - 2 ) ( x + 5 )$ 
B)  $( 3 x + 2 ) ( x - 5 )$ 
C)  $( 3 x + 2 ) ( x + 5 )$ 
D)  $( 18 x + 2 ) ( x + 5 )$ 
A)  $( 3 x - 2 ) ( x + 5 )$ 
B)  $( 3 x + 2 ) ( x - 5 )$ 
C)  $( 3 x + 2 ) ( x + 5 )$ 
D)  $( 18 x + 2 ) ( x + 5 )$

Question 20

Solve the problem.
-Let $f ( x ) = x ^ { 2 } + x - 12$. Find all values $x$ for which $f ( x ) = 0$.

Accepted Answer

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

Factor the GCF out of the given expression. - $4 t ^ { 2 } - 8 t - 8$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -A triangle is 5 centimeters wider than it is tall. The area is 102 square cm. Find the width (length of the base).

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $5 x ^ { 2 } + 13 x + 6$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 4 } - s ^ { 4 }$

Find the GCF. - $64 a ^ { 8 } b ^ { 4 } , 56 a ^ { 6 } b ^ { 8 }$

Factor by grouping. - $x ^ { 3 } - x ^ { 2 } + 9 x - 9$

Solve the problem. -Let $f ( x ) = x ^ { 2 } - x - 56$ . Find all values $x$ for which $f ( x ) = 0$ .

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $5 x ^ { 5 } + 20 x ^ { 4 } - 105 x ^ { 3 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $3 x ^ { 2 } + 3 x - 18$

Factor the GCF out of the given expression. - $x ^ { 8 } - 9 x ^ { 3 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $25 x ^ { 2 } - 49$

Find the GCF. -30,36

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $8 x ^ { 2 } - 8$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -A rock falls from a tower that is 464 feet high. As it is falling, its height is given by the function $h ( t ) = - 16 t ^ { 2 } + 464 t$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $3 x ^ { 8 } - 15 x ^ { 7 } + 12 x ^ { 6 }$

Find the missing value such that the given binomial is a factor of the given polynomial. - $x ^ { 2 } - 18 x + ? , x - 9$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $3 x ^ { 3 } - 12 x ^ { 2 } - 135 x$

Factor the GCF out of the given expression. - $3 x ( x + 5 ) + 2 ( x + 5 )$

Solve the problem. -Let $f ( x ) = x ^ { 2 } + x - 12$ . Find all values $x$ for which $f ( x ) = 0$ .

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Exponents and Polynomials

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring and Quadratic Equations

Factor the GCF out of the given expression. - 4t2−8t−84 t ^ { 2 } - 8 t - 84t2−8t−8

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -A triangle is 5 centimeters wider than it is tall. The area is 102 square cm. Find the width (length of the base).

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 5x2+13x+65 x ^ { 2 } + 13 x + 65x2+13x+6

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - x4−s4x ^ { 4 } - s ^ { 4 }x4−s4

Find the GCF. - 64a8b4,56a6b864 a ^ { 8 } b ^ { 4 } , 56 a ^ { 6 } b ^ { 8 }64a8b4,56a6b8

Factor by grouping. - x3−x2+9x−9x ^ { 3 } - x ^ { 2 } + 9 x - 9x3−x2+9x−9

Solve the problem. -Let f(x)=x2−x−56f ( x ) = x ^ { 2 } - x - 56f(x)=x2−x−56 . Find all values xxx for which f(x)=0f ( x ) = 0f(x)=0 .

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 5x5+20x4−105x35 x ^ { 5 } + 20 x ^ { 4 } - 105 x ^ { 3 }5x5+20x4−105x3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 3x2+3x−183 x ^ { 2 } + 3 x - 183x2+3x−18

Factor the GCF out of the given expression. - x8−9x3x ^ { 8 } - 9 x ^ { 3 }x8−9x3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 25x2−4925 x ^ { 2 } - 4925x2−49