Question 1

Factor out the GCF from the polynomial.
-$$3 x ^ { 6 } y + 12 x ^ { 4 }$$

Accepted Answer

A)  $x ^ { 4 } \left( 3 x ^ { 2 } y + 12 \right)$ 
B)  $3 x ^ { 4 } \left( x ^ { 2 } y + 4 \right)$ 
C)  $3 x ^ { 5 } ( x y + 4 x )$ 
D)  $3 x ^ { 4 } y \left( x ^ { 2 } + 4 \right)$ 
A)  $x ^ { 4 } \left( 3 x ^ { 2 } y + 12 \right)$ 
B)  $3 x ^ { 4 } \left( x ^ { 2 } y + 4 \right)$ 
C)  $3 x ^ { 5 } ( x y + 4 x )$ 
D)  $3 x ^ { 4 } y \left( x ^ { 2 } + 4 \right)$

Question 2

Factor completely.
-$$x ^ { 2 } - x - 6$$

Accepted Answer

A)  $( x + 1 ) ( x - 6 )$ 
B)  $( x + 3 ) ( x - 2 )$ 
C)  $( x + 2 ) ( x - 3 )$ 
D)  prime 
A)  $( x + 1 ) ( x - 6 )$ 
B)  $( x + 3 ) ( x - 2 )$ 
C)  $( x + 2 ) ( x - 3 )$ 
D)  prime

Question 3

Factor out the GCF from the polynomial.
-$60 x ^ { 9 } y ^ { 8 } + 72 x ^ { 6 } y ^ { 5 } - 60 x ^ { 2 } y ^ { 3 }$

Accepted Answer

A)  $12 x ^ { 2 } y ^ { 3 } \left( 5 x ^ { 7 } y ^ { 5 } + 6 x ^ { 4 } y ^ { 2 } - 5 \right)$ 
B)  $12 \left( 5 x ^ { 9 } y ^ { 8 } + 6 x ^ { 6 } y ^ { 5 } - 5 x ^ { 2 } y ^ { 3 } \right)$ 
C)  $12 x ^ { 2 } \left( 5 x ^ { 7 } y ^ { 8 } + 6 x ^ { 4 } y ^ { 5 } - 5 y ^ { 3 } \right)$ 
D)  cannot be factored 
A)  $12 x ^ { 2 } y ^ { 3 } \left( 5 x ^ { 7 } y ^ { 5 } + 6 x ^ { 4 } y ^ { 2 } - 5 \right)$ 
B)  $12 \left( 5 x ^ { 9 } y ^ { 8 } + 6 x ^ { 6 } y ^ { 5 } - 5 x ^ { 2 } y ^ { 3 } \right)$ 
C)  $12 x ^ { 2 } \left( 5 x ^ { 7 } y ^ { 8 } + 6 x ^ { 4 } y ^ { 5 } - 5 y ^ { 3 } \right)$ 
D)  cannot be factored

Question 4

Factor completely.
-x3y + 6x2y2 + 8xy3

Accepted Answer

A)  xy(x + 4y)(x + 2y) 
B)  y(x + 4y)(xy + 2y2) 
C)  x(xy + 4y2)(x + 2y) 
D)  xy(x2 + 6x + 8y2) 
A)  xy(x + 4y)(x + 2y) 
B)  y(x + 4y)(xy + 2y2) 
C)  x(xy + 4y2)(x + 2y) 
D)  xy(x2 + 6x + 8y2)

Question 5

Factor out the GCF from the polynomial.
-$8 m ^ { 9 } - 18 m ^ { 5 } + 10 m ^ { 2 }$

Accepted Answer

A)  $2 \left( 4 m ^ { 9 } - 9 m ^ { 5 } + 5 m ^ { 2 } \right)$ 
B)  $- 2 m ^ { 2 } \left( 4 m ^ { 7 } + 9 m ^ { 3 } - 5 \right)$ 
C)  $m ^ { 2 } \left( 8 m ^ { 7 } - 18 m ^ { 3 } + 10 \right)$ 
D)  $2 m ^ { 2 } \left( 4 m ^ { 7 } - 9 m ^ { 3 } + 5 \right)$ 
A)  $2 \left( 4 m ^ { 9 } - 9 m ^ { 5 } + 5 m ^ { 2 } \right)$ 
B)  $- 2 m ^ { 2 } \left( 4 m ^ { 7 } + 9 m ^ { 3 } - 5 \right)$ 
C)  $m ^ { 2 } \left( 8 m ^ { 7 } - 18 m ^ { 3 } + 10 \right)$ 
D)  $2 m ^ { 2 } \left( 4 m ^ { 7 } - 9 m ^ { 3 } + 5 \right)$

Question 6

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$5 \mathrm { x } ^ { 2 } + 9 \mathrm { x } + 2$

Accepted Answer

A)  prime 
B)  $( 5 x + 2 ) ( x - 1 )$ 
C)  $( 5 x + 1 ) ( x - 2 )$ 
D)  $( 5 x - 1 ) ( x + 2 )$ 
A)  prime 
B)  $( 5 x + 2 ) ( x - 1 )$ 
C)  $( 5 x + 1 ) ( x - 2 )$ 
D)  $( 5 x - 1 ) ( x + 2 )$

Question 7

Factor completely.
-x2 + 4xy - 96y2

Accepted Answer

A)  (x - 12y)(x + 8y) 
B)  prime 
C)  (x + 12y)(x - 8y) 
D)  (x - 12y)(x + y) 
A)  (x - 12y)(x + 8y) 
B)  prime 
C)  (x + 12y)(x - 8y) 
D)  (x - 12y)(x + y)

Question 8

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$10 y ^ { 2 } + 21 y + 9$

Accepted Answer

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

Question 9

Write a polynomial for the length of the rectangle.
-

Accepted Answer

A)  $x ^ { 2 } + 8$ 
B)  $x - 5$ 
C)  $x ^ { 2 } - 6 x - 8 x + 35$ 
D)  $x + 40$ 
A)  $x ^ { 2 } + 8$ 
B)  $x - 5$ 
C)  $x ^ { 2 } - 6 x - 8 x + 35$ 
D)  $x + 40$

Question 10

Factor the polynomial using the negative of the greatest common factor.
-$- 10 x ^ { 2 } - 6$

Accepted Answer

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

Question 11

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$14 x ^ { 2 } - 49 x - 28$

Accepted Answer

A)  $7 ( 2 x + 1 ) ( x - 4 )$ 
B)  prime 
C)  $( 14 x - 7 ) ( x + 4 )$ 
D)  $7 ( 2 x - 1 ) ( x + 4 )$ 
A)  $7 ( 2 x + 1 ) ( x - 4 )$ 
B)  prime 
C)  $( 14 x - 7 ) ( x + 4 )$ 
D)  $7 ( 2 x - 1 ) ( x + 4 )$

Question 12

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$24 x ^ { 2 } - 104 x - 80$

Accepted Answer

A)  $( 24 x + 16 ) ( x - 5 )$ 
B)  $8 ( 3 x + 2 ) ( x - 5 )$ 
C)  $8 ( 3 x - 2 ) ( x + 5 )$ 
D)  prime 
A)  $( 24 x + 16 ) ( x - 5 )$ 
B)  $8 ( 3 x + 2 ) ( x - 5 )$ 
C)  $8 ( 3 x - 2 ) ( x + 5 )$ 
D)  prime

Question 13

Factor the polynomial using the greatest common binomial factor.
-$$x ( x + 13 ) - 3 ( x + 13 )$$

Accepted Answer

A)  $( x + 13 ) ( x + 3 )$ 
B)  $( x - 13 ) ( x + 3 )$ 
C)  $\left( x ^ { 2 } + 13 x \right) ( 3 x + 39 )$ 
D)  $( x + 13 ) ( x - 3 )$ 
A)  $( x + 13 ) ( x + 3 )$ 
B)  $( x - 13 ) ( x + 3 )$ 
C)  $\left( x ^ { 2 } + 13 x \right) ( 3 x + 39 )$ 
D)  $( x + 13 ) ( x - 3 )$

Question 14

Factor out the GCF from the polynomial.
-$$8 x + 8$$

Accepted Answer

A)  $8 x + 1$ 
B)  $8 ( x + 8 )$ 
C)  $8 ( x + 1 )$ 
D)  $64 x$ 
A)  $8 x + 1$ 
B)  $8 ( x + 8 )$ 
C)  $8 ( x + 1 )$ 
D)  $64 x$

Question 15

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$4 y ^ { 2 } + 18 y - 10$$

Accepted Answer

A)  $2 ( 2 y + 1 ) ( y - 5 )$ 
B)  prime 
C)  $2 ( 2 y - 1 ) ( y + 5 )$ 
D)  $( 4 y - 2 ) ( y + 5 )$ 
A)  $2 ( 2 y + 1 ) ( y - 5 )$ 
B)  prime 
C)  $2 ( 2 y - 1 ) ( y + 5 )$ 
D)  $( 4 y - 2 ) ( y + 5 )$

Question 16

Factor the polynomial using the negative of the greatest common factor.
-$$- 24 x ^ { 2 } + 16$$

Accepted Answer

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

Question 17

Factor completely. If unfactorable, indicate that the polynomial is prime.
-$49 x ^ { 2 } - 16$

Accepted Answer

A)  $( 7 x - 4 ) ^ { 2 }$ 
B)  prime 
C)  $( 7 x + 4 ) ^ { 2 }$ 
D)  $( 7 x + 4 ) ( 7 x - 4 )$ 
A)  $( 7 x - 4 ) ^ { 2 }$ 
B)  prime 
C)  $( 7 x + 4 ) ^ { 2 }$ 
D)  $( 7 x + 4 ) ( 7 x - 4 )$

Question 18

Factor completely.
-5x6 + 40x5 - 45x4

Accepted Answer

A)  5x4(x - 1)(x + 9) 
B)  5x4(x2 + 8x - 9) 
C)  x4(5x - 5)(x + 9) 
D)  x4(x - 1)(5x + 45) 
A)  5x4(x - 1)(x + 9) 
B)  5x4(x2 + 8x - 9) 
C)  x4(5x - 5)(x + 9) 
D)  x4(x - 1)(5x + 45)

Question 19

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$x ^ { 6 } - 3 x ^ { 5 } - 18 x ^ { 4 }$

Accepted Answer

A)  $x ^ { 4 } ( x + 3 ) ( x + 6 )$ 
B)  $x ^ { 3 } \left( x ^ { 2 } - 3 x - 18 \right)$ 
C)  $x ^ { 4 } ( x - 3 ) ( x - 6 )$ 
D)  $x ^ { 4 } ( x + 3 ) ( x - 6 )$ 
A)  $x ^ { 4 } ( x + 3 ) ( x + 6 )$ 
B)  $x ^ { 3 } \left( x ^ { 2 } - 3 x - 18 \right)$ 
C)  $x ^ { 4 } ( x - 3 ) ( x - 6 )$ 
D)  $x ^ { 4 } ( x + 3 ) ( x - 6 )$

Question 20

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$$3 x ^ { 2 } + 34 x + 11$$

Accepted Answer

A)  $( 3 x + 1 ) ( x + 11 )$ 
B)  prime 
C)  $( 3 x - 1 ) ( x - 11 )$ 
D)  $( 3 x + 11 ) ( x + 1 )$ 
A)  $( 3 x + 1 ) ( x + 11 )$ 
B)  prime 
C)  $( 3 x - 1 ) ( x - 11 )$ 
D)  $( 3 x + 11 ) ( x + 1 )$

Factor out the GCF from the polynomial. - $3 x ^ { 6 } y + 12 x ^ { 4 }$

Factor completely. - $x ^ { 2 } - x - 6$

Factor out the GCF from the polynomial. - $60 x ^ { 9 } y ^ { 8 } + 72 x ^ { 6 } y ^ { 5 } - 60 x ^ { 2 } y ^ { 3 }$

Factor completely. -x³y + 6x²y² + 8xy³

Factor out the GCF from the polynomial. - $8 m ^ { 9 } - 18 m ^ { 5 } + 10 m ^ { 2 }$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $5 \mathrm { x } ^ { 2 } + 9 \mathrm { x } + 2$

Factor completely. -x² + 4xy - 96y²

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $10 y ^ { 2 } + 21 y + 9$

Write a polynomial for the length of the rectangle. -

Factor the polynomial using the negative of the greatest common factor. - $- 10 x ^ { 2 } - 6$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $14 x ^ { 2 } - 49 x - 28$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $24 x ^ { 2 } - 104 x - 80$

Factor the polynomial using the greatest common binomial factor. - $x ( x + 13 ) - 3 ( x + 13 )$

Factor out the GCF from the polynomial. - $8 x + 8$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $4 y ^ { 2 } + 18 y - 10$

Factor the polynomial using the negative of the greatest common factor. - $- 24 x ^ { 2 } + 16$

Factor completely. If unfactorable, indicate that the polynomial is prime. - $49 x ^ { 2 } - 16$

Factor completely. -5x6 + 40x5 - 45x4

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $x ^ { 6 } - 3 x ^ { 5 } - 18 x ^ { 4 }$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $3 x ^ { 2 } + 34 x + 11$

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

Basics of Functions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 6: Factoring Polynomials

Factor out the GCF from the polynomial. - 3x6y+12x43 x ^ { 6 } y + 12 x ^ { 4 }3x6y+12x4

Factor completely. - x2−x−6x ^ { 2 } - x - 6x2−x−6

Factor out the GCF from the polynomial. - 60x9y8+72x6y5−60x2y360 x ^ { 9 } y ^ { 8 } + 72 x ^ { 6 } y ^ { 5 } - 60 x ^ { 2 } y ^ { 3 }60x9y8+72x6y5−60x2y3

Factor completely. -x3y + 6x2y2 + 8xy3

Factor out the GCF from the polynomial. - 8m9−18m5+10m28 m ^ { 9 } - 18 m ^ { 5 } + 10 m ^ { 2 }8m9−18m5+10m2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 5x2+9x+25 \mathrm { x } ^ { 2 } + 9 \mathrm { x } + 25x2+9x+2

Factor completely. -x2 + 4xy - 96y2

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 10y2+21y+910 y ^ { 2 } + 21 y + 910y2+21y+9