Question 1

Factor the four-term polynomial by grouping.
-$x y - 6 y z + 9 x - 54 z$

Accepted Answer

A)  $( y - 6 ) ( x + 9 z )$ 
B)  $( y + 9 ) ( x - 6 z )$ 
C)  $( y + 6 ) ( x - 9 z )$ 
D)  $( y - 9 ) ( x + 6 z )$ 
A)  $( y - 6 ) ( x + 9 z )$ 
B)  $( y + 9 ) ( x - 6 z )$ 
C)  $( y + 6 ) ( x - 9 z )$ 
D)  $( y - 9 ) ( x + 6 z )$

Question 2

Factor the polynomial by grouping.
-$2 x ^ { 4 } - 3 x ^ { 2 } + 4 x ^ { 2 } - 6$

Accepted Answer

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

Question 3

Factor the binomial completely.
-$121 - w ^ { 2 }$

Accepted Answer

A)  prime 
B)  $( 11 - w ) ( 11 + w )$ 
C)  $( 11 + w ) ^ { 2 }$ 
D)  $( 11 - w ) ^ { 2 }$ 
A)  prime 
B)  $( 11 - w ) ( 11 + w )$ 
C)  $( 11 + w ) ^ { 2 }$ 
D)  $( 11 - w ) ^ { 2 }$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

A)  $( x - 8 ) \left( x ^ { 2 } + 8 x + 64 \right)$ 
B)  $( x - 8 ) \left( x ^ { 2 } + 64 \right)$ 
C)  $( x + 8 ) \left( x ^ { 2 } - 8 x + 64 \right)$ 
D)  $( x + 512 ) ( x + 1 ) ( x - 1 )$ 
A)  $( x - 8 ) \left( x ^ { 2 } + 8 x + 64 \right)$ 
B)  $( x - 8 ) \left( x ^ { 2 } + 64 \right)$ 
C)  $( x + 8 ) \left( x ^ { 2 } - 8 x + 64 \right)$ 
D)  $( x + 512 ) ( x + 1 ) ( x - 1 )$

Question 6

Factor a negative number or a GCF with a negative coefficient from the polynomial.
-$- 5 x ^ { 6 } + 10 x ^ { 5 } - 5 x ^ { 3 }$

Accepted Answer

A)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } + 1 \right)$ 
B)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } - 1 \right)$ 
C)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } + x \right)$ 
D)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } - x \right)$ 
A)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } + 1 \right)$ 
B)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } - 1 \right)$ 
C)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } + x \right)$ 
D)  $- 5 x ^ { 3 } \left( x ^ { 3 } - 2 x ^ { 2 } - x \right)$

Question 7

Factor completely.
-$24 x ^ { 2 } + 14 x y + 2 y ^ { 2 }$

Accepted Answer

A)  $( 6 x + 2 y ) ( 4 x + y )$ 
B)  prime 
C)  $2 ( 3 x - y ) ( 4 x - y )$ 
D)  $2 ( 3 x + y ) ( 4 x + y )$ 
A)  $( 6 x + 2 y ) ( 4 x + y )$ 
B)  prime 
C)  $2 ( 3 x - y ) ( 4 x - y )$ 
D)  $2 ( 3 x + y ) ( 4 x + y )$

Question 8

Factor the sum or difference of two cubes.
-$192 x ^ { 3 } + 375$

Accepted Answer

A)  $3 ( 4 x + 5 ) \left( 16 x ^ { 2 } + 25 \right)$ 
B)  $3 ( 4 x - 5 ) \left( 16 x ^ { 2 } + 20 x + 25 \right)$ 
C)  $3 ( 4 x + 5 ) \left( 16 x ^ { 2 } - 20 x + 25 \right)$ 
D)  $3 \left( 64 x ^ { 3 } + 125 \right)$ 
A)  $3 ( 4 x + 5 ) \left( 16 x ^ { 2 } + 25 \right)$ 
B)  $3 ( 4 x - 5 ) \left( 16 x ^ { 2 } + 20 x + 25 \right)$ 
C)  $3 ( 4 x + 5 ) \left( 16 x ^ { 2 } - 20 x + 25 \right)$ 
D)  $3 \left( 64 x ^ { 3 } + 125 \right)$

Question 9

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 3 } - x ^ { 2 } - 20 x$

Accepted Answer

A)  $x ( x + 4 ) ( x - 5 )$ 
B)  $\left( x ^ { 2 } + 1 \right) ( x - 20 )$ 
C)  $x ( x + 5 ) ( x - 4 )$ 
D)  prime 
A)  $x ( x + 4 ) ( x - 5 )$ 
B)  $\left( x ^ { 2 } + 1 \right) ( x - 20 )$ 
C)  $x ( x + 5 ) ( x - 4 )$ 
D)  prime

Question 10

Factor the trinomial by grouping.
-$8 x ^ { 2 } - 6 x y - 9 y ^ { 2 }$

Accepted Answer

A)  $( 4 x - 3 y ) ( 2 x + 3 y )$ 
B)  $( 8 x + 3 y ) ( x - 3 y )$ 
C)  prime 
D)  $( 4 x + 3 y ) ( 2 x - 3 y )$ 
A)  $( 4 x - 3 y ) ( 2 x + 3 y )$ 
B)  $( 8 x + 3 y ) ( x - 3 y )$ 
C)  prime 
D)  $( 4 x + 3 y ) ( 2 x - 3 y )$

Question 11

Solve the equation.
-$( 22 - 0.8 x ) ( 5 - 0.4 x ) = 0$

Accepted Answer

A)  $27.5,12.5$ 
B)  $27.5,0.2$ 
C)  22,5 
D)  $0.8,5$ 
A)  $27.5,12.5$ 
B)  $27.5,0.2$ 
C)  22,5 
D)  $0.8,5$

Question 12

Solve the equation.
-$x ^ { 2 } + 3 x = 0$

Accepted Answer

A)  3 
B)  $0 , - 3$ 
C)  $- 3$ 
D)  0,3 
A)  3 
B)  $0 , - 3$ 
C)  $- 3$ 
D)  0,3

Question 13

Solve the equation.
-$5 x ^ { 3 } - 3 x ^ { 2 } - 8 x = 0$

Accepted Answer

A)  $\frac { 5 } { 8 } , - 1,0$ 
B)  $\frac { 5 } { 8 } , 1$ 
C)  $\frac { 5 } { 8 } , 0$ 
D)  $\frac { 8 } { 5 } , - 1,0$ 
A)  $\frac { 5 } { 8 } , - 1,0$ 
B)  $\frac { 5 } { 8 } , 1$ 
C)  $\frac { 5 } { 8 } , 0$ 
D)  $\frac { 8 } { 5 } , - 1,0$

Question 14

Factor the trinomial by grouping.
-$10 x ^ { 2 } - 19 x y + 6 y ^ { 2 }$

Accepted Answer

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

Question 15

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$200 - 2 x ^ { 2 }$

Accepted Answer

A)  $2 ( 10 + x ) ( 10 - x )$ 
B)  $2 ( x + 10 ) ( x - 10 )$ 
C)  prime 
D)  $2 ( x - 10 ) ^ { 2 }$ 
A)  $2 ( 10 + x ) ( 10 - x )$ 
B)  $2 ( x + 10 ) ( x - 10 )$ 
C)  prime 
D)  $2 ( x - 10 ) ^ { 2 }$

Question 16

Find the GCF for the list.
-36,15

Accepted Answer

A)  6 
B)  15 
C)  1 
D)  3 
A)  6 
B)  15 
C)  1 
D)  3

Question 17

Factor the perfect square trinomial completely.
-$x ^ { 3 } + 20 x ^ { 2 } + 100 x$

Accepted Answer

A)  $x ( x + 10 ) ^ { 2 }$ 
B)  prime 
C)  $x ( x - 10 ) ^ { 2 }$ 
D)  $x ( x + 10 ) ( x - 10 )$ 
A)  $x ( x + 10 ) ^ { 2 }$ 
B)  prime 
C)  $x ( x - 10 ) ^ { 2 }$ 
D)  $x ( x + 10 ) ( x - 10 )$

Question 18

Find a positive value of the given variable so that the trinomial is factorable.
-$13 y ^ { 2 } + b y - 1 ; b =$ ?

Accepted Answer

A)  12 
B)  15 
C)  14 
D)  13 
A)  12 
B)  15 
C)  14 
D)  13

Question 19

Factor the trinomial completely. If the polynomial cannot be factored, write "prime."
-$x ^ { 4 } - 10 x ^ { 3 } + 24 x ^ { 2 }$

Accepted Answer

A)  $x ^ { 2 } ( x - 4 ) ( x + 6 )$ 
B)  $x ^ { 2 } ( x + 4 ) ( x - 6 )$ 
C)  $x ^ { - 4 } \left( x ^ { 2 } - 10 x + 24 \right)$ 
D)  $x ^ { 2 } ( x - 4 ) ( x - 6 )$ 
A)  $x ^ { 2 } ( x - 4 ) ( x + 6 )$ 
B)  $x ^ { 2 } ( x + 4 ) ( x - 6 )$ 
C)  $x ^ { - 4 } \left( x ^ { 2 } - 10 x + 24 \right)$ 
D)  $x ^ { 2 } ( x - 4 ) ( x - 6 )$

Question 20

Solve.
-If the sides of a square are increased by 2 meters, the area becomes 36 square meters. Find the length of a side of the original square.

Accepted Answer

A)  4 m 
B)  8 m 
C)  2 m 
D)  6 m 
A)  4 m 
B)  8 m 
C)  2 m 
D)  6 m

Factor the four-term polynomial by grouping. - $x y - 6 y z + 9 x - 54 z$

Factor the polynomial by grouping. - $2 x ^ { 4 } - 3 x ^ { 2 } + 4 x ^ { 2 } - 6$

Factor the binomial completely. - $121 - w ^ { 2 }$

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

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

Factor a negative number or a GCF with a negative coefficient from the polynomial. - $- 5 x ^ { 6 } + 10 x ^ { 5 } - 5 x ^ { 3 }$

Factor completely. - $24 x ^ { 2 } + 14 x y + 2 y ^ { 2 }$

Factor the sum or difference of two cubes. - $192 x ^ { 3 } + 375$

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 3 } - x ^ { 2 } - 20 x$

Factor the trinomial by grouping. - $8 x ^ { 2 } - 6 x y - 9 y ^ { 2 }$

Solve the equation. - $( 22 - 0.8 x ) ( 5 - 0.4 x ) = 0$

Solve the equation. - $x ^ { 2 } + 3 x = 0$

Solve the equation. - $5 x ^ { 3 } - 3 x ^ { 2 } - 8 x = 0$

Factor the trinomial by grouping. - $10 x ^ { 2 } - 19 x y + 6 y ^ { 2 }$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $200 - 2 x ^ { 2 }$

Find the GCF for the list. -36,15

Factor the perfect square trinomial completely. - $x ^ { 3 } + 20 x ^ { 2 } + 100 x$

Find a positive value of the given variable so that the trinomial is factorable. - $13 y ^ { 2 } + b y - 1 ; b =$ ?

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - $x ^ { 4 } - 10 x ^ { 3 } + 24 x ^ { 2 }$

Solve. -If the sides of a square are increased by 2 meters, the area becomes 36 square meters. Find the length of a side of the original square.

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

Factor the four-term polynomial by grouping. - xy−6yz+9x−54zx y - 6 y z + 9 x - 54 zxy−6yz+9x−54z

Factor the polynomial by grouping. - 2x4−3x2+4x2−62 x ^ { 4 } - 3 x ^ { 2 } + 4 x ^ { 2 } - 62x4−3x2+4x2−6

Factor the binomial completely. - 121−w2121 - w ^ { 2 }121−w2

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

Factor the sum or difference of two cubes. - x3−512x ^ { 3 } - 512x3−512

Factor a negative number or a GCF with a negative coefficient from the polynomial. - −5x6+10x5−5x3- 5 x ^ { 6 } + 10 x ^ { 5 } - 5 x ^ { 3 }−5x6+10x5−5x3

Factor completely. - 24x2+14xy+2y224 x ^ { 2 } + 14 x y + 2 y ^ { 2 }24x2+14xy+2y2

Factor the sum or difference of two cubes. - 192x3+375192 x ^ { 3 } + 375192x3+375

Factor the trinomial completely. If the polynomial cannot be factored, write "prime." - x3−x2−20xx ^ { 3 } - x ^ { 2 } - 20 xx3−x2−20x

Factor the trinomial by grouping. - 8x2−6xy−9y28 x ^ { 2 } - 6 x y - 9 y ^ { 2 }8x2−6xy−9y2

Solve the equation. - (22−0.8x)(5−0.4x)=0( 22 - 0.8 x ) ( 5 - 0.4 x ) = 0(22−0.8x)(5−0.4x)=0

Solve the equation. - x2+3x=0x ^ { 2 } + 3 x = 0x2+3x=0

Solve the equation. - 5x3−3x2−8x=05 x ^ { 3 } - 3 x ^ { 2 } - 8 x = 05x3−3x2−8x=0

Factor the trinomial by grouping. - 10x2−19xy+6y210 x ^ { 2 } - 19 x y + 6 y ^ { 2 }10x2−19xy+6y2

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - 200−2x2200 - 2 x ^ { 2 }200−2x2