Question 1

Factor by grouping.
-$10 x ^ { 6 } - 25 x ^ { 3 } + 8 x ^ { 3 } - 20$

Accepted Answer

A)  $\left( 5 x ^ { 6 } + 4 \right) ( 2 x - 5 )$ 
B)  $\left( 10 x ^ { 3 } - 4 \right) \left( x ^ { 3 } + 5 \right)$ 
C)  $\left( 5 x ^ { 3 } + 4 \right) \left( 2 x ^ { 3 } - 5 \right)$ 
D)  $\left( 5 x ^ { 3 } - 4 \right) \left( 2 x ^ { 3 } + 5 \right)$ 
A)  $\left( 5 x ^ { 6 } + 4 \right) ( 2 x - 5 )$ 
B)  $\left( 10 x ^ { 3 } - 4 \right) \left( x ^ { 3 } + 5 \right)$ 
C)  $\left( 5 x ^ { 3 } + 4 \right) \left( 2 x ^ { 3 } - 5 \right)$ 
D)  $\left( 5 x ^ { 3 } - 4 \right) \left( 2 x ^ { 3 } + 5 \right)$

Question 2

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is
prime.
-$$2 x ^ { 2 } + 6 x - 20$$

Accepted Answer

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

Question 3

Factor completely.
-x2 + 34x + 35

Accepted Answer

A)  (x + 35)(x - 1) 
B)  (x - 7)(x + 5) 
C)  (x + 7)(x - 5) 
D)  prime 
A)  (x + 35)(x - 1) 
B)  (x - 7)(x + 5) 
C)  (x + 7)(x - 5) 
D)  prime

Question 4

Factor completely. If unfactorable, indicate that the polynomial is prime.
-$$x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 }$$

Accepted Answer

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

Question 5

Write a polynomial for the width of the rectangle.
-Write a polynomial for the width of the rectangle.

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 }$ 
B)  $x + 9 x ^ { 2 }$ 
C)  $x + 3$ 
D)  $3 x ^ { 3 } + 6 x ^ { 2 }$ 
A)  $x ^ { 3 } + 3 x ^ { 2 }$ 
B)  $x + 9 x ^ { 2 }$ 
C)  $x + 3$ 
D)  $3 x ^ { 3 } + 6 x ^ { 2 }$

Question 6

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$$9 x ^ { 2 } - 39 x - 30$$

Accepted Answer

A)  prime 
B)  $3 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 9 x + 6 ) ( x - 5 )$ 
D)  $3 ( 3 x - 2 ) ( x + 5 )$ 
A)  prime 
B)  $3 ( 3 x + 2 ) ( x - 5 )$ 
C)  $( 9 x + 6 ) ( x - 5 )$ 
D)  $3 ( 3 x - 2 ) ( x + 5 )$

Question 7

Find the greatest common factor of the monomials.
-$14 y ^ { 4 }$ and $56 y ^ { 7 }$

Accepted Answer

A)  $14 \mathrm { y } ^ { 4 }$ 
B)  $14 y ^ { 3 }$ 
C)  $56 \mathrm { y } ^ { 4 }$ 
D)  $784 \mathrm { y } ^ { 3 }$ 
A)  $14 \mathrm { y } ^ { 4 }$ 
B)  $14 y ^ { 3 }$ 
C)  $56 \mathrm { y } ^ { 4 }$ 
D)  $784 \mathrm { y } ^ { 3 }$

Question 8

Solve the problem.
-Express the combined areas of the three rectangles as the product of two binomials.

Accepted Answer

A)  $( 5 x + 1 ) ( 3 x + 16 )$ 
B)  $( 5 x + 2 ) ( 3 x + 8 )$ 
C)  $15 x ^ { 2 } + 52$ 
D)  $( 5 x + 8 ) ( 3 x + 2 )$ 
A)  $( 5 x + 1 ) ( 3 x + 16 )$ 
B)  $( 5 x + 2 ) ( 3 x + 8 )$ 
C)  $15 x ^ { 2 } + 52$ 
D)  $( 5 x + 8 ) ( 3 x + 2 )$

Question 9

Factor completely. If unfactorable, indicate that the polynomial is prime.
-$36 \mathrm { k } ^ { 2 } - 49 \mathrm {~m} ^ { 2 }$

Accepted Answer

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

Question 10

Factor out the GCF from the polynomial.
-$$17 x ^ { 4 } - 11$$

Accepted Answer

A)  cannot be factored 
B)  $17 \left( x ^ { 4 } - 11 \right)$ 
C)  $17 \left( x ^ { 4 } - 187 \right)$ 
D)  $17 \left( x ^ { 4 } - \frac { 11 } { 17 } \right)$ 
A)  cannot be factored 
B)  $17 \left( x ^ { 4 } - 11 \right)$ 
C)  $17 \left( x ^ { 4 } - 187 \right)$ 
D)  $17 \left( x ^ { 4 } - \frac { 11 } { 17 } \right)$

Question 11

Factor out the GCF from the polynomial.
-$20 \mathrm { x } + 10$

Accepted Answer

A)  $10 ( 2 x )$ 
B)  $10 ( 2 x + 1 )$ 
C)  $5 ( 4 x + 2 )$ 
D)  $2 ( 10 x + 5 )$ 
A)  $10 ( 2 x )$ 
B)  $10 ( 2 x + 1 )$ 
C)  $5 ( 4 x + 2 )$ 
D)  $2 ( 10 x + 5 )$

Question 12

Find the greatest common factor of the monomials.
-$16 x ^ { 10 }$ and $20 x ^ { 6 }$

Accepted Answer

A)  $4 x ^ { 6 }$ 
B)  $20 x ^ { 4 }$ 
C)  $16 x ^ { 6 }$ 
D)  $4 \mathrm { x } ^ { 10 }$ 
A)  $4 x ^ { 6 }$ 
B)  $20 x ^ { 4 }$ 
C)  $16 x ^ { 6 }$ 
D)  $4 \mathrm { x } ^ { 10 }$

Question 13

Factor by grouping.
-$$3 x ^ { 2 } + 9 x y - 4 x y - 12 y ^ { 2 }$$

Accepted Answer

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

Question 14

Factor out the GCF from the polynomial.
-$18 x ^ { 9 } y ^ { 9 } + 63 x ^ { 7 } y ^ { 7 } + 54 x ^ { 5 } y ^ { 5 }$

Accepted Answer

A)  $9 x ^ { 5 } y ^ { 5 } \left( 2 x ^ { 4 } y ^ { 4 } + 7 x ^ { 2 } y ^ { 2 } + 6 \right)$ 
B)  $9 \left( 2 x ^ { 9 } y ^ { 9 } + 7 x ^ { 7 } y ^ { 7 } + 6 x ^ { 5 } y ^ { 5 } \right)$ 
C)  $- 9 x ^ { 5 } y ^ { 5 } \left( - 2 x ^ { 4 } y ^ { 4 } + 7 x ^ { 2 } y ^ { 2 } - 6 \right)$ 
D)  $9 x ^ { 5 } \left( 2 x ^ { 4 } y ^ { 9 } + 7 x ^ { 2 } y ^ { 7 } + 6 y ^ { 5 } \right)$ 
A)  $9 x ^ { 5 } y ^ { 5 } \left( 2 x ^ { 4 } y ^ { 4 } + 7 x ^ { 2 } y ^ { 2 } + 6 \right)$ 
B)  $9 \left( 2 x ^ { 9 } y ^ { 9 } + 7 x ^ { 7 } y ^ { 7 } + 6 x ^ { 5 } y ^ { 5 } \right)$ 
C)  $- 9 x ^ { 5 } y ^ { 5 } \left( - 2 x ^ { 4 } y ^ { 4 } + 7 x ^ { 2 } y ^ { 2 } - 6 \right)$ 
D)  $9 x ^ { 5 } \left( 2 x ^ { 4 } y ^ { 9 } + 7 x ^ { 2 } y ^ { 7 } + 6 y ^ { 5 } \right)$

Question 15

Factor completely.
-x2 - x - 45

Accepted Answer

A)  (x + 5)(x - 9) 
B)  prime 
C)  (x - 5)(x + 9) 
D)  (x - 45)(x + 1) 
A)  (x + 5)(x - 9) 
B)  prime 
C)  (x - 5)(x + 9) 
D)  (x - 45)(x + 1)

Question 16

Factor out the GCF from the polynomial.
-$18 \mathrm { p } + 9 \mathrm { q } - 9$

Accepted Answer

A)  $9 p ( 2 + q - 1 )$ 
B)  cannot be factored 
C)  $9 ( 2 p + q - 1 )$ 
D)  $9 ( 2 p + q )$ 
A)  $9 p ( 2 + q - 1 )$ 
B)  cannot be factored 
C)  $9 ( 2 p + q - 1 )$ 
D)  $9 ( 2 p + q )$

Question 17

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime.
-$x ^ { 4 } - 4 x ^ { 3 } - 21 x ^ { 2 }$

Accepted Answer

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

Question 18

Factor completely.
-2x2- 6xy - 8y2

Accepted Answer

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

Question 19

Factor completely. If unfactorable, indicate that the polynomial is prime.
-$$- x ^ { 2 } + 6 x + 40$$

Accepted Answer

A)  $( x - 4 ) ( x + 10 )$ 
B)  prime 
C)  $- ( x + 4 ) ( x - 10 )$ 
D)  $- ( x - 4 ) ( x + 10 )$ 
A)  $( x - 4 ) ( x + 10 )$ 
B)  prime 
C)  $- ( x + 4 ) ( x - 10 )$ 
D)  $- ( x - 4 ) ( x + 10 )$

Question 20

Find the greatest common factor of the monomials.
-$- 6 x ^ { 10 }$ and $8 x ^ { 7 }$

Accepted Answer

A)  $- 8 x ^ { 3 }$ 
B)  $2 x ^ { 7 }$ 
C)  $2 x ^ { 10 }$ 
D)  $- 6 x ^ { 7 }$ 
A)  $- 8 x ^ { 3 }$ 
B)  $2 x ^ { 7 }$ 
C)  $2 x ^ { 10 }$ 
D)  $- 6 x ^ { 7 }$

Factor by grouping. - $10 x ^ { 6 } - 25 x ^ { 3 } + 8 x ^ { 3 } - 20$

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $2 x ^ { 2 } + 6 x - 20$

Factor completely. -x² + 34x + 35

Factor completely. If unfactorable, indicate that the polynomial is prime. - $x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 }$

Write a polynomial for the width of the rectangle. -Write a polynomial for the width of the rectangle.

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $9 x ^ { 2 } - 39 x - 30$

Find the greatest common factor of the monomials. - $14 y ^ { 4 }$ and $56 y ^ { 7 }$

Solve the problem. -Express the combined areas of the three rectangles as the product of two binomials.

Factor completely. If unfactorable, indicate that the polynomial is prime. - $36 \mathrm { k } ^ { 2 } - 49 \mathrm {~m} ^ { 2 }$

Factor out the GCF from the polynomial. - $17 x ^ { 4 } - 11$

Factor out the GCF from the polynomial. - $20 \mathrm { x } + 10$

Find the greatest common factor of the monomials. - $16 x ^ { 10 }$ and $20 x ^ { 6 }$

Factor by grouping. - $3 x ^ { 2 } + 9 x y - 4 x y - 12 y ^ { 2 }$

Factor out the GCF from the polynomial. - $18 x ^ { 9 } y ^ { 9 } + 63 x ^ { 7 } y ^ { 7 } + 54 x ^ { 5 } y ^ { 5 }$

Factor completely. -x² - x - 45

Factor out the GCF from the polynomial. - $18 \mathrm { p } + 9 \mathrm { q } - 9$

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - $x ^ { 4 } - 4 x ^ { 3 } - 21 x ^ { 2 }$

Factor completely. -2x²- 6xy - 8y²

Factor completely. If unfactorable, indicate that the polynomial is prime. - $- x ^ { 2 } + 6 x + 40$

Find the greatest common factor of the monomials. - $- 6 x ^ { 10 }$ and $8 x ^ { 7 }$

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 by grouping. - 10x6−25x3+8x3−2010 x ^ { 6 } - 25 x ^ { 3 } + 8 x ^ { 3 } - 2010x6−25x3+8x3−20

Factor completely using the trial and error method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 2x2+6x−202 x ^ { 2 } + 6 x - 202x2+6x−20

Factor completely. -x2 + 34x + 35

Factor completely. If unfactorable, indicate that the polynomial is prime. - x2−29x+181x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 }x2−92​x+811​

Write a polynomial for the width of the rectangle. -Write a polynomial for the width of the rectangle.

Factor completely using the grouping method to factor trinomials. If unfactorable, indicate that the polynomial is prime. - 9x2−39x−309 x ^ { 2 } - 39 x - 309x2−39x−30

Find the greatest common factor of the monomials. - 14y414 y ^ { 4 }14y4 and 56y756 y ^ { 7 }56y7