Question 1

Factor.
-$10 y ^ { 2 } + 45 y - 25$

Accepted Answer

A)  $( 2 y - 1 ) ( 5 y + 25 )$ 
B)  $( 10 y - 5 ) ( y + 5 )$ 
C)  $5 ( 2 y - 1 ) ( y + 5 )$ 
D)  $5 ( 2 y + 1 ) ( y - 5 )$ 
A)  $( 2 y - 1 ) ( 5 y + 25 )$ 
B)  $( 10 y - 5 ) ( y + 5 )$ 
C)  $5 ( 2 y - 1 ) ( y + 5 )$ 
D)  $5 ( 2 y + 1 ) ( y - 5 )$

Question 2

Factor.
-$5 x ( 5 x - 2 ) - 5 ( 5 x - 2 )$

Accepted Answer

A)  $( 6 x - 5 ) ( 5 x - 2 )$ 
B)  $( 6 x + 5 ) ( 5 x + 2 )$ 
C)  $( 30 x + 5 ) ( x + 2 )$ 
D)  $( 30 x - 5 ) ( x - 2 )$ 
A)  $( 6 x - 5 ) ( 5 x - 2 )$ 
B)  $( 6 x + 5 ) ( 5 x + 2 )$ 
C)  $( 30 x + 5 ) ( x + 2 )$ 
D)  $( 30 x - 5 ) ( x - 2 )$

Question 3

Factor.
-9x ${ } ^ { 2 } - 9 \mathrm { x } - 54$

Accepted Answer

A)  $9 ( x - 2 ) ( x + 3 )$ 
B)  $( x + 2 ) ( 9 x - 27 )$ 
C)  $( 9 x + 18 ) ( x - 3 )$ 
D)  $9 ( x + 2 ) ( x - 3 )$ 
A)  $9 ( x - 2 ) ( x + 3 )$ 
B)  $( x + 2 ) ( 9 x - 27 )$ 
C)  $( 9 x + 18 ) ( x - 3 )$ 
D)  $9 ( x + 2 ) ( x - 3 )$

Question 4

Factor.
-$64 y ^ { 9 } - z ^ { 9 }$

Accepted Answer

A)  $\left( 16 y ^ { 3 } - z ^ { 3 } \right) \left( 4 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
B)  $\left( 4 y ^ { 3 } - z ^ { 3 } \right) \left( 16 y ^ { 6 } - 4 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
C)  $\left( 16 y ^ { 3 } + z ^ { 3 } \right) \left( 4 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
D)  $\left( 4 y ^ { 3 } - z ^ { 3 } \right) \left( 16 y ^ { 6 } + 4 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
A)  $\left( 16 y ^ { 3 } - z ^ { 3 } \right) \left( 4 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
B)  $\left( 4 y ^ { 3 } - z ^ { 3 } \right) \left( 16 y ^ { 6 } - 4 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
C)  $\left( 16 y ^ { 3 } + z ^ { 3 } \right) \left( 4 y ^ { 6 } + y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$ 
D)  $\left( 4 y ^ { 3 } - z ^ { 3 } \right) \left( 16 y ^ { 6 } + 4 y ^ { 3 } z ^ { 3 } + z ^ { 6 } \right)$

Question 5

Factor.
-$x ^ { 2 } + 3 x y - 108 y ^ { 2 }$

Accepted Answer

A)  $( x + 12 y ) ( x - 9 y )$ 
B)  $( x - y ) ( x + 9 y )$ 
C)  $( x - 12 y ) ( x + y )$ 
D)  $( x - 12 y ) ( x + 9 y )$ 
A)  $( x + 12 y ) ( x - 9 y )$ 
B)  $( x - y ) ( x + 9 y )$ 
C)  $( x - 12 y ) ( x + y )$ 
D)  $( x - 12 y ) ( x + 9 y )$

Question 6

Factor.
-$15 y ^ { 2 } + 16 y + 4$

Accepted Answer

A)  $( 3 y - 2 ) ( 5 y - 2 )$ 
B)  $( 15 y + 2 ) ( y + 2 )$ 
C)  $( 3 y + 2 ) ( 5 y + 2 )$ 
D)  Prime 
A)  $( 3 y - 2 ) ( 5 y - 2 )$ 
B)  $( 15 y + 2 ) ( y + 2 )$ 
C)  $( 3 y + 2 ) ( 5 y + 2 )$ 
D)  Prime

Question 7

Factor.
-$8 z ^ { 3 } - 6 z ^ { 2 } - 9 z$

Accepted Answer

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

Question 8

Factor.
-$x ^ { 2 } + 3 x y - 28 y ^ { 2 }$

Accepted Answer

A)  $( x - 7 y ) ( x + y )$ 
B)  $( x + 7 y ) ( x - 4 y )$ 
C)  $( x - 7 y ) ( x + 4 y )$ 
D)  $( x - y ) ( x + 4 y )$ 
A)  $( x - 7 y ) ( x + y )$ 
B)  $( x + 7 y ) ( x - 4 y )$ 
C)  $( x - 7 y ) ( x + 4 y )$ 
D)  $( x - y ) ( x + 4 y )$

Question 9

Factor completely.
-$36 k ^ { 2 } - 49 m ^ { 2 }$

Accepted Answer

A)  $( 36 \mathrm { k } + \mathrm { m } ) ( \mathrm { k } - 49 \mathrm {~m} )$ 
B)  $( 6 \mathrm { k } - 7 \mathrm {~m} ) ^ { 2 }$ 
C)  $( 6 \mathrm { k } + 7 \mathrm {~m} ) ^ { 2 }$ 
D)  $( 6 \mathrm { k } + 7 \mathrm {~m} ) ( 6 \mathrm { k } - 7 \mathrm {~m} )$ 
A)  $( 36 \mathrm { k } + \mathrm { m } ) ( \mathrm { k } - 49 \mathrm {~m} )$ 
B)  $( 6 \mathrm { k } - 7 \mathrm {~m} ) ^ { 2 }$ 
C)  $( 6 \mathrm { k } + 7 \mathrm {~m} ) ^ { 2 }$ 
D)  $( 6 \mathrm { k } + 7 \mathrm {~m} ) ( 6 \mathrm { k } - 7 \mathrm {~m} )$

Question 10

Factor completely.
-$$a ^ { 2 } - 50 a b + 625 b ^ { 2 }$$

Accepted Answer

A)  Prime 
B)  $( a + 25 b ) ( a - 25 b )$ 
C)  $( a + 25 b ) ^ { 2 }$ 
D)  $( a - 25 b ) ^ { 2 }$ 
A)  Prime 
B)  $( a + 25 b ) ( a - 25 b )$ 
C)  $( a + 25 b ) ^ { 2 }$ 
D)  $( a - 25 b ) ^ { 2 }$

Question 11

Factor.
-$6 x ^ { 2 } + 17 x + 12$

Accepted Answer

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

Question 12

Factor completely.
-$$4 x ^ { 2 } + 25$$

Accepted Answer

A)  prime 
B)  $( 2 x + 5 ) ( 2 x - 5 )$ 
C)  $( 2 x + 5 ) ^ { 2 }$ 
D)  $( 2 x - 5 ) ^ { 2 }$ 
A)  prime 
B)  $( 2 x + 5 ) ( 2 x - 5 )$ 
C)  $( 2 x + 5 ) ^ { 2 }$ 
D)  $( 2 x - 5 ) ^ { 2 }$

Question 13

Factor completely.
-$$5 x ^ { 8 } - 1280$$

Accepted Answer

A)  $5 \left( x ^ { 4 } + 16 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
B)  $5 \left( x ^ { 4 } - 16 \right) ^ { 2 }$ 
C)  $5 \left( x ^ { 4 } + 16 \right) \left( x ^ { 4 } - 16 \right)$ 
D)  $\left( 5 x ^ { 4 } + 80 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
A)  $5 \left( x ^ { 4 } + 16 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$ 
B)  $5 \left( x ^ { 4 } - 16 \right) ^ { 2 }$ 
C)  $5 \left( x ^ { 4 } + 16 \right) \left( x ^ { 4 } - 16 \right)$ 
D)  $\left( 5 x ^ { 4 } + 80 \right) \left( x ^ { 2 } + 4 \right) ( x + 2 ) ( x - 2 )$

Question 14

Factor completely.
-$$x ^ { 2 } - 12 x y + 36 y ^ { 2 }$$

Accepted Answer

A)  Prime 
B)  $( x + 6 y ) ^ { 2 }$ 
C)  $( x - 6 y ) ( x + 6 y )$ 
D)  $( x - 6 y ) ^ { 2 }$ 
A)  Prime 
B)  $( x + 6 y ) ^ { 2 }$ 
C)  $( x - 6 y ) ( x + 6 y )$ 
D)  $( x - 6 y ) ^ { 2 }$

Question 15

Determine whether the following is a trinomial square.
-$$x ^ { 2 } - 4 x - 4$$

Accepted Answer

A) True 
 B)False

Question 16

Factor.
-$18 - 3 x - x ^ { 2 }$

Accepted Answer

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

Question 17

Factor.
-$$3 x ^ { 3 } + 6 x ^ { 2 } - 45 x$$

Accepted Answer

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

Question 18

Factor.
-$54 k ^ { 3 } m - 128 m ^ { 4 }$

Accepted Answer

A)  $\left( 6 \mathrm {~km} - 8 \mathrm {~m} ^ { 2 } \right) \left( 9 \mathrm { k } ^ { 2 } + 16 \mathrm {~m} ^ { 2 } \right)$ 
B)  $2 m ( 27 k - 4 m ) \left( k ^ { 2 } + 12 k m + 16 m ^ { 2 } \right)$ 
C)  $2 m ( 3 k - 4 m ) \left( 9 k ^ { 2 } + 12 k m + 16 m ^ { 2 } \right)$ 
D)  $2 m \left( 3 k + 4 m ^ { 2 } \right) \left( 9 k ^ { 2 } - 12 k m + 16 k ^ { 2 } \right)$ 
A)  $\left( 6 \mathrm {~km} - 8 \mathrm {~m} ^ { 2 } \right) \left( 9 \mathrm { k } ^ { 2 } + 16 \mathrm {~m} ^ { 2 } \right)$ 
B)  $2 m ( 27 k - 4 m ) \left( k ^ { 2 } + 12 k m + 16 m ^ { 2 } \right)$ 
C)  $2 m ( 3 k - 4 m ) \left( 9 k ^ { 2 } + 12 k m + 16 m ^ { 2 } \right)$ 
D)  $2 m \left( 3 k + 4 m ^ { 2 } \right) \left( 9 k ^ { 2 } - 12 k m + 16 k ^ { 2 } \right)$

Question 19

Factor by grouping.
-$15 x ^ { 4 } + 20 x ^ { 2 } - 12 x ^ { 2 } - 16$

Accepted Answer

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

Question 20

Factor.
-$$\mathrm { y } ^ { 2 } + 0.2 \mathrm { y } - 0.35$$

Accepted Answer

A)  $( y - 0.7 ) ( y + 0.5 )$ 
B)  $( \mathrm { y } + 0.7 ) ( \mathrm { y } - 0.5 )$ 
C)  $( y + 0.1 ) ^ { 2 }$ 
D)  $( \mathrm { y } - 0.7 ) ( \mathrm { y } - 0.5 )$ 
A)  $( y - 0.7 ) ( y + 0.5 )$ 
B)  $( \mathrm { y } + 0.7 ) ( \mathrm { y } - 0.5 )$ 
C)  $( y + 0.1 ) ^ { 2 }$ 
D)  $( \mathrm { y } - 0.7 ) ( \mathrm { y } - 0.5 )$

Factor. - $10 y ^ { 2 } + 45 y - 25$

Factor. - $5 x ( 5 x - 2 ) - 5 ( 5 x - 2 )$

Factor. -9x ${ } ^ { 2 } - 9 \mathrm { x } - 54$

Factor. - $64 y ^ { 9 } - z ^ { 9 }$

Factor. - $x ^ { 2 } + 3 x y - 108 y ^ { 2 }$

Factor. - $15 y ^ { 2 } + 16 y + 4$

Factor. - $8 z ^ { 3 } - 6 z ^ { 2 } - 9 z$

Factor. - $x ^ { 2 } + 3 x y - 28 y ^ { 2 }$

Factor completely. - $36 k ^ { 2 } - 49 m ^ { 2 }$

Factor completely. - $a ^ { 2 } - 50 a b + 625 b ^ { 2 }$

Factor. - $6 x ^ { 2 } + 17 x + 12$

Factor completely. - $4 x ^ { 2 } + 25$

Factor completely. - $5 x ^ { 8 } - 1280$

Factor completely. - $x ^ { 2 } - 12 x y + 36 y ^ { 2 }$

Determine whether the following is a trinomial square. - $x ^ { 2 } - 4 x - 4$

Factor. - $18 - 3 x - x ^ { 2 }$

Factor. - $3 x ^ { 3 } + 6 x ^ { 2 } - 45 x$

Factor. - $54 k ^ { 3 } m - 128 m ^ { 4 }$

Factor by grouping. - $15 x ^ { 4 } + 20 x ^ { 2 } - 12 x ^ { 2 } - 16$

Factor. - $\mathrm { y } ^ { 2 } + 0.2 \mathrm { y } - 0.35$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Filters

Exam 5: Polynomials: Factoring

Factor. - 10y2+45y−2510 y ^ { 2 } + 45 y - 2510y2+45y−25

Factor. - 5x(5x−2)−5(5x−2)5 x ( 5 x - 2 ) - 5 ( 5 x - 2 )5x(5x−2)−5(5x−2)

Factor. -9x 2−9x−54{ } ^ { 2 } - 9 \mathrm { x } - 542−9x−54

Factor. - 64y9−z964 y ^ { 9 } - z ^ { 9 }64y9−z9

Factor. - x2+3xy−108y2x ^ { 2 } + 3 x y - 108 y ^ { 2 }x2+3xy−108y2

Factor. - 15y2+16y+415 y ^ { 2 } + 16 y + 415y2+16y+4

Factor. - 8z3−6z2−9z8 z ^ { 3 } - 6 z ^ { 2 } - 9 z8z3−6z2−9z

Factor. - x2+3xy−28y2x ^ { 2 } + 3 x y - 28 y ^ { 2 }x2+3xy−28y2

Factor completely. - 36k2−49m236 k ^ { 2 } - 49 m ^ { 2 }36k2−49m2

Factor completely. - a2−50ab+625b2a ^ { 2 } - 50 a b + 625 b ^ { 2 }a2−50ab+625b2

Factor. - 6x2+17x+126 x ^ { 2 } + 17 x + 126x2+17x+12

Factor completely. - 4x2+254 x ^ { 2 } + 254x2+25

Factor completely. - 5x8−12805 x ^ { 8 } - 12805x8−1280

Factor completely. - x2−12xy+36y2x ^ { 2 } - 12 x y + 36 y ^ { 2 }x2−12xy+36y2

Determine whether the following is a trinomial square. - x2−4x−4x ^ { 2 } - 4 x - 4x2−4x−4

Factor. - 18−3x−x218 - 3 x - x ^ { 2 }18−3x−x2

Factor. - 3x3+6x2−45x3 x ^ { 3 } + 6 x ^ { 2 } - 45 x3x3+6x2−45x

Factor. - 54k3m−128m454 k ^ { 3 } m - 128 m ^ { 4 }54k3m−128m4

Factor by grouping. - 15x4+20x2−12x2−1615 x ^ { 4 } + 20 x ^ { 2 } - 12 x ^ { 2 } - 1615x4+20x2−12x2−16

Factor. - y2+0.2y−0.35\mathrm { y } ^ { 2 } + 0.2 \mathrm { y } - 0.35y2+0.2y−0.35