Question 1

Factor the GCF out of the given expression.
-$$- 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x$$

Accepted Answer

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

Question 2

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$- x ^ { 2 } - 2 x + 80$$

Accepted Answer

A)  $( x + 8 ) ( x - 10 )$ 
B)  $- ( x - 8 ) ( x - 10 )$ 
C)  $- ( x - 8 ) ( x + 10 )$ 
D)  Prime 
A)  $( x + 8 ) ( x - 10 )$ 
B)  $- ( x - 8 ) ( x - 10 )$ 
C)  $- ( x - 8 ) ( x + 10 )$ 
D)  Prime

Question 3

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$8 x ^ { 3 } - 6 x ^ { 2 } - 9 x$$

Accepted Answer

A)  $\left( x ^ { 2 } - 3 \right) ( 8 x + 3 )$ 
B)  $x ( 4 x + 3 ) ( 2 x - 3 )$ 
C)  $x ( 8 x + 1 ) ( x - 9 )$ 
D)  $( 4 x - 3 ) ( 2 x + 3 )$ 
A)  $\left( x ^ { 2 } - 3 \right) ( 8 x + 3 )$ 
B)  $x ( 4 x + 3 ) ( 2 x - 3 )$ 
C)  $x ( 8 x + 1 ) ( x - 9 )$ 
D)  $( 4 x - 3 ) ( 2 x + 3 )$

Question 4

Solve the problem.
-Let $f ( x ) = x ^ { 2 } + 12 x + 29$. Find all values $x$ for which $f ( x ) = 2$.

Accepted Answer

A)  $- 3,9$ 
B)  $3 , - 9$ 
C)  $- 9 , - 3$ 
D)  3,9 
A)  $- 3,9$ 
B)  $3 , - 9$ 
C)  $- 9 , - 3$ 
D)  3,9

Question 5

Find the GCF.
-120,200

Accepted Answer

A)  8 
B)  40 
C)  5 
D)  20 
A)  8 
B)  40 
C)  5 
D)  20

Question 6

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$x ^ { 5 } y ^ { 2 } - 6 x ^ { 4 } y ^ { 3 } - 16 x ^ { 3 } y ^ { 4 }$

Accepted Answer

A)  $x ^ { 3 } y ^ { 2 } ( x - 8 y ) ( x + y )$ 
B)  $x ^ { 3 } y ^ { 2 } ( x + y ) ( x - 2 y )$ 
C)  $x ^ { 3 } y ^ { 2 } ( x - 8 y ) ( x + 2 y )$ 
D)  $x ^ { 3 } y ^ { 2 } ( x + 8 y ) ( x - 2 y )$ 
A)  $x ^ { 3 } y ^ { 2 } ( x - 8 y ) ( x + y )$ 
B)  $x ^ { 3 } y ^ { 2 } ( x + y ) ( x - 2 y )$ 
C)  $x ^ { 3 } y ^ { 2 } ( x - 8 y ) ( x + 2 y )$ 
D)  $x ^ { 3 } y ^ { 2 } ( x + 8 y ) ( x - 2 y )$

Question 7

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$3 x ^ { 3 } - 375 y ^ { 3 }$

Accepted Answer

A)  $3 ( x - 5 y ) \left( x ^ { 2 } + 25 y ^ { 2 } \right)$ 
B)  $( 3 x - 5 y ) \left( x ^ { 2 } + 5 y + 75 y ^ { 2 } \right)$ 
C)  $3 ( x - 5 y ) \left( x ^ { 2 } + 5 x y + 25 y ^ { 2 } \right)$ 
D)  $3 ( x + 5 y ) \left( x ^ { 2 } - 5 x y + 25 y ^ { 2 } \right)$ 
A)  $3 ( x - 5 y ) \left( x ^ { 2 } + 25 y ^ { 2 } \right)$ 
B)  $( 3 x - 5 y ) \left( x ^ { 2 } + 5 y + 75 y ^ { 2 } \right)$ 
C)  $3 ( x - 5 y ) \left( x ^ { 2 } + 5 x y + 25 y ^ { 2 } \right)$ 
D)  $3 ( x + 5 y ) \left( x ^ { 2 } - 5 x y + 25 y ^ { 2 } \right)$

Question 8

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 3 } - 216$$

Accepted Answer

A)  $( x - 6 ) \left( x ^ { 2 } + 36 \right)$ 
B)  $( x - 6 ) \left( x ^ { 2 } + 6 x + 36 \right.$ 
C)  $( x + 6 ) \left( x ^ { 2 } - 6 x + 36 \right)$ 
D)  $( x + 216 ) \left( x ^ { 2 } - 1 \right)$ 
A)  $( x - 6 ) \left( x ^ { 2 } + 36 \right)$ 
B)  $( x - 6 ) \left( x ^ { 2 } + 6 x + 36 \right.$ 
C)  $( x + 6 ) \left( x ^ { 2 } - 6 x + 36 \right)$ 
D)  $( x + 216 ) \left( x ^ { 2 } - 1 \right)$

Question 9

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-Susan is 7 years older than her brother Bob. If the product of their ages is 638 $\text { how old is Susan }$

Accepted Answer

A)  7 
B)  29 
C)  22 
D)  30 
A)  7 
B)  29 
C)  22 
D)  30

Question 10

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$250 \mathrm { k } ^ { 3 } \mathrm {~m} - 128 \mathrm {~m} ^ { 4 }$

Accepted Answer

A)  $2 \mathrm {~m} ( 5 \mathrm { k } - 4 \mathrm {~m} ) \left( 25 \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$ 
B)  $2 m \left( 5 \mathrm { k } + 4 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } - 20 \mathrm {~km} + 16 \mathrm {~km} { } ^ { 2 } \right)$ 
C)  $2 \mathrm {~m} ( 125 \mathrm { k } - 4 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$ 
D)  $\left( 10 \mathrm {~km} - 8 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } + 16 \mathrm {~m} ^ { 2 } \right)$ 
A)  $2 \mathrm {~m} ( 5 \mathrm { k } - 4 \mathrm {~m} ) \left( 25 \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$ 
B)  $2 m \left( 5 \mathrm { k } + 4 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } - 20 \mathrm {~km} + 16 \mathrm {~km} { } ^ { 2 } \right)$ 
C)  $2 \mathrm {~m} ( 125 \mathrm { k } - 4 \mathrm {~m} ) \left( \mathrm { k } ^ { 2 } + 20 \mathrm {~km} + 16 \mathrm {~m} ^ { 2 } \right)$ 
D)  $\left( 10 \mathrm {~km} - 8 \mathrm {~m} ^ { 2 } \right) \left( 25 \mathrm { k } ^ { 2 } + 16 \mathrm {~m} ^ { 2 } \right)$

Question 11

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$8 \mathrm {~s} ^ { 3 } + 1$

Accepted Answer

A)  $( 2 \mathrm {~s} + 1 ) \left( 4 \mathrm {~s} ^ { 2 } + 1 \right)$ 
B)  $( 2 s + 1 ) \left( 4 s ^ { 2 } - 2 s + 1 \right)$ 
C)  $( 8 s + 1 ) \left( s ^ { 2 } - 2 s + 1 \right)$ 
D)  $( 2 \mathrm {~s} - 1 ) \left( 4 \mathrm {~s} ^ { 2 } + 2 \mathrm {~s} + 1 \right)$ 
A)  $( 2 \mathrm {~s} + 1 ) \left( 4 \mathrm {~s} ^ { 2 } + 1 \right)$ 
B)  $( 2 s + 1 ) \left( 4 s ^ { 2 } - 2 s + 1 \right)$ 
C)  $( 8 s + 1 ) \left( s ^ { 2 } - 2 s + 1 \right)$ 
D)  $( 2 \mathrm {~s} - 1 ) \left( 4 \mathrm {~s} ^ { 2 } + 2 \mathrm {~s} + 1 \right)$

Question 12

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } y ^ { 2 } + 7 x y - 44$$

Accepted Answer

A)  $( x y - 11 ) ( x y + 4 )$ 
B)  $( x y - 11 ) ( x y + 1 )$ 
C)  $( x y + 11 ) ( x y - 4 )$ 
D)  Prime 
A)  $( x y - 11 ) ( x y + 4 )$ 
B)  $( x y - 11 ) ( x y + 1 )$ 
C)  $( x y + 11 ) ( x y - 4 )$ 
D)  Prime

Question 13

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$$x ^ { 2 } + 23 x - 24$$

Accepted Answer

A)  $( x + 6 ) ( x - 4 )$ 
B)  $( x + 24 ) ( x - 1 )$ 
C)  $( x - 6 ) ( x + 4 )$ 
D)  Prime 
A)  $( x + 6 ) ( x - 4 )$ 
B)  $( x + 24 ) ( x - 1 )$ 
C)  $( x - 6 ) ( x + 4 )$ 
D)  Prime

Question 14

Find the GCF.
-,108,486

Accepted Answer

A)  18 
B)  50 
C)  54 
D)  2 
A)  18 
B)  50 
C)  54 
D)  2

Question 15

Determine which factoring technique is appropriate for the given polynomial.
-$$x ^ { 3 } + 729 y ^ { 3 }$$

Accepted Answer

A)  sum of cubes 
B)  sum of squares 
C)  difference of cubes 
D)  factoring by grouping 
A)  sum of cubes 
B)  sum of squares 
C)  difference of cubes 
D)  factoring by grouping

Question 16

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$32 x ^ { 4 } - 50 y ^ { 2 }$

Accepted Answer

A)  $2 \left( 4 x ^ { 2 } - 5 y \right) ^ { 2 }$ 
B)  $\left( 8 x ^ { 2 } + 10 y \right) \left( 4 x ^ { 2 } - 5 y \right)$ 
C)  $2 \left( 4 x ^ { 2 } + 5 y \right) ^ { 2 }$ 
D)  $2 \left( 4 x ^ { 2 } + 5 y \right) \left( 4 x ^ { 2 } - 5 y \right)$ 
A)  $2 \left( 4 x ^ { 2 } - 5 y \right) ^ { 2 }$ 
B)  $\left( 8 x ^ { 2 } + 10 y \right) \left( 4 x ^ { 2 } - 5 y \right)$ 
C)  $2 \left( 4 x ^ { 2 } + 5 y \right) ^ { 2 }$ 
D)  $2 \left( 4 x ^ { 2 } + 5 y \right) \left( 4 x ^ { 2 } - 5 y \right)$

Question 17

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x.
-If a ball is thrown upward from the ground with an initial velocity of 128 feet per second, its height after t seconds is given by the function $h ( t ) = - 16 t ^ { 2 } + 128 t$

Accepted Answer

A)  4 seconds 
B)  8 seconds 
C)  112 seconds 
D)  64 seconds 
A)  4 seconds 
B)  8 seconds 
C)  112 seconds 
D)  64 seconds

Question 18

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$343 y ^ { 3 } - 512$

Accepted Answer

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

Question 19

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ
-$729 - 1000 x ^ { 3 }$

Accepted Answer

A)  $( 729 - 10 x ) \left( 1 + 90 x + 100 x ^ { 2 } \right)$ 
B)  $( 9 + 10 x ) \left( 81 - 90 x + 100 x ^ { 2 } \right)$ 
C)  $( 9 - 10 x ) \left( 81 + 100 x ^ { 2 } \right)$ 
D)  $( 9 - 10 x ) \left( 81 + 90 x + 100 x ^ { 2 } \right)$ 
A)  $( 729 - 10 x ) \left( 1 + 90 x + 100 x ^ { 2 } \right)$ 
B)  $( 9 + 10 x ) \left( 81 - 90 x + 100 x ^ { 2 } \right)$ 
C)  $( 9 - 10 x ) \left( 81 + 100 x ^ { 2 } \right)$ 
D)  $( 9 - 10 x ) \left( 81 + 90 x + 100 x ^ { 2 } \right)$

Question 20

Determine which factoring technique is appropriate for the given polynomial.
-$$3 x ^ { 2 } y ^ { 3 } + 15 x y ^ { 2 } - 27 x y$$

Accepted Answer

A)  factor out GCF 
B)  difference of squares 
C)  sum of squares 
D)  factoring by grouping 
A)  factor out GCF 
B)  difference of squares 
C)  sum of squares 
D)  factoring by grouping

Factor the GCF out of the given expression. - $- 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $- x ^ { 2 } - 2 x + 80$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $8 x ^ { 3 } - 6 x ^ { 2 } - 9 x$

Solve the problem. -Let $f ( x ) = x ^ { 2 } + 12 x + 29$ . Find all values $x$ for which $f ( x ) = 2$ .

Find the GCF. -120,200

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 5 } y ^ { 2 } - 6 x ^ { 4 } y ^ { 3 } - 16 x ^ { 3 } y ^ { 4 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $3 x ^ { 3 } - 375 y ^ { 3 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 3 } - 216$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -Susan is 7 years older than her brother Bob. If the product of their ages is 638 $\text { how old is Susan }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $250 \mathrm { k } ^ { 3 } \mathrm {~m} - 128 \mathrm {~m} ^ { 4 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $8 \mathrm {~s} ^ { 3 } + 1$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } y ^ { 2 } + 7 x y - 44$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $x ^ { 2 } + 23 x - 24$

Find the GCF. -,108,486

Determine which factoring technique is appropriate for the given polynomial. - $x ^ { 3 } + 729 y ^ { 3 }$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $32 x ^ { 4 } - 50 y ^ { 2 }$

Find all fixed points for the function by setting the function equal to x and solving the resulting equation for x. -If a ball is thrown upward from the ground with an initial velocity of 128 feet per second, its height after t seconds is given by the function $h ( t ) = - 16 t ^ { 2 } + 128 t$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $343 y ^ { 3 } - 512$

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - $729 - 1000 x ^ { 3 }$

Determine which factoring technique is appropriate for the given polynomial. - $3 x ^ { 2 } y ^ { 3 } + 15 x y ^ { 2 } - 27 x y$

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. - −6x3−12x2+9x- 6 x ^ { 3 } - 12 x ^ { 2 } + 9 x−6x3−12x2+9x

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - −x2−2x+80- x ^ { 2 } - 2 x + 80−x2−2x+80

Factor completely. If the polynomial cannot be factored, write ʺprime.ʺ - 8x3−6x2−9x8 x ^ { 3 } - 6 x ^ { 2 } - 9 x8x3−6x2−9x

Solve the problem. -Let f(x)=x2+12x+29f ( x ) = x ^ { 2 } + 12 x + 29f(x)=x2+12x+29 . Find all values xxx for which f(x)=2f ( x ) = 2f(x)=2 .