Question 1

Factor the trinomial completely.
-$6 a ^ { 2 } - 7 a b - 3 b ^ { 2 }$

Accepted Answer

A) (6a + b)(a - 3b) 
B) (3a + b)(2a - 3b) 
C) (3a - b)(2a + 3b) 
D) prime 
A) (6a + b)(a - 3b) 
B) (3a + b)(2a - 3b) 
C) (3a - b)(2a + 3b) 
D) prime

Question 2

Solve the equation.
-15 $15 d ^ { 2 } - 2 d = 0$

Accepted Answer

A)  $\frac { 15 } { 2 } , 0$ 
B)  $- \frac { 2 } { 15 } , 0$ 
C)  $- \frac { 15 } { 2 } , 0$ 
D)  $\frac { 2 } { 15 } , 0$ 
A)  $\frac { 15 } { 2 } , 0$ 
B)  $- \frac { 2 } { 15 } , 0$ 
C)  $- \frac { 15 } { 2 } , 0$ 
D)  $\frac { 2 } { 15 } , 0$

Question 3

Represent the given condition using a single variable, x.
-Three consecutive odd integers

Accepted Answer

A) x and x + 2, if x is an odd integer 
B) x + 2, x + 4, and x + 6, if x is an odd integer 
C) x, x + 2, and x + 4, if x is an odd integer 
D) x, x + 1, and x + 2, if x is an odd integer 
A) x and x + 2, if x is an odd integer 
B) x + 2, x + 4, and x + 6, if x is an odd integer 
C) x, x + 2, and x + 4, if x is an odd integer 
D) x, x + 1, and x + 2, if x is an odd integer

Question 4

Factor a -1 from the polynomial.
-6a - b - 5

Accepted Answer

A) -1(6a + b + 5) 
B) -1(-6a + b + 5) 
C) -1(-6a + b - 5) 
D) -1(-6a - b + 5) 
A) -1(6a + b + 5) 
B) -1(-6a + b + 5) 
C) -1(-6a + b - 5) 
D) -1(-6a - b + 5)

Question 5

Solve the equation.
-(4y + 5)(7y + 6)= 0

Accepted Answer

A) 1, -1 
B)  $- \frac { 5 } { 4 } , - \frac { 6 } { 7 }$ 
C)   $- 4 , - \frac { 7 } { 6 }$ 
D)  $\frac { 5 } { 4 } , \frac { 6 } { 7 }$ 
A) 1, -1 
B)  $- \frac { 5 } { 4 } , - \frac { 6 } { 7 }$ 
C)   $- 4 , - \frac { 7 } { 6 }$ 
D)  $\frac { 5 } { 4 } , \frac { 6 } { 7 }$

Question 6

Factor the binomial completely.
-$75 x ^ { 2 } y - 108 y$

Accepted Answer

A) 3y(5x + 6)(5x - 6) 
B)  $3 y ( 5 x + 6 ) ^ { 2 }$ 
C)  $3 y ( 5 x - 6 ) ^ { 2 }$ 
D) prime polynomial 
A) 3y(5x + 6)(5x - 6) 
B)  $3 y ( 5 x + 6 ) ^ { 2 }$ 
C)  $3 y ( 5 x - 6 ) ^ { 2 }$ 
D) prime polynomial

Question 7

Find the GCF for the list.
-$x ^ { 6 } y ^ { 8 } , x ^ { 5 } y ^ { 7 } , x y ^ { 8 } , x ^ { 2 } y ^ { 6 }$

Accepted Answer

A)  $x ^ { 2 } y ^ { 6 }$ 
B)  $x ^ { 2 } y ^ { 2 }$ 
C) xy 
D)  $x y ^ { 6 }$ 
A)  $x ^ { 2 } y ^ { 6 }$ 
B)  $x ^ { 2 } y ^ { 2 }$ 
C) xy 
D)  $x y ^ { 6 }$

Question 8

Factor the four-term polynomial by grouping.
-6x - 66 + xy - 11y

Accepted Answer

A) (x - 11)(6 + y) 
B) (x - 11y)(6 + y) 
C) (y - 11)(6x + y) 
D) (y - 11)(x + 6) 
A) (x - 11)(6 + y) 
B) (x - 11y)(6 + y) 
C) (y - 11)(6x + y) 
D) (y - 11)(x + 6)

Question 9

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$4 t ^ { 2 } + t - 5$

Accepted Answer

A) (4t + 5)(t - 1) 
B) (4t - 5)(t + 1) 
C) (4t + 1)(t - 5) 
D) (4t - 1)(t + 5) 
A) (4t + 5)(t - 1) 
B) (4t - 5)(t + 1) 
C) (4t + 1)(t - 5) 
D) (4t - 1)(t + 5)

Question 10

Find the GCF for the list.
-$10 \mathrm {~m} ^ { 4 } , 40 \mathrm {~m} ^ { 9 } , 100 \mathrm {~m} ^ { 5 }$

Accepted Answer

A)  $10 \mathrm {~m} ^ { 4 }$ 
B)  $400 \mathrm {~m} ^ { 5 }$ 
C)  $40 \mathrm {~m} ^ { 4 }$ 
D)  $10 \mathrm {~m} ^ { 5 }$ 
A)  $10 \mathrm {~m} ^ { 4 }$ 
B)  $400 \mathrm {~m} ^ { 5 }$ 
C)  $40 \mathrm {~m} ^ { 4 }$ 
D)  $10 \mathrm {~m} ^ { 5 }$

Question 11

Solve the equation.
-$20 y ^ { 2 } + 31 y + 12 = 0$

Accepted Answer

A)  $\frac { 4 } { 5 } , \frac { 3 } { 4 }$ 
B)   $- \frac { 4 } { 5 } , - \frac { 3 } { 4 }$ 
C)   $- \frac { 1 } { 5 } , - \frac { 1 } { 4 }$ 
D)  $\frac { 4 } { 5 } , - \frac { 3 } { 4 }$ 
A)  $\frac { 4 } { 5 } , \frac { 3 } { 4 }$ 
B)   $- \frac { 4 } { 5 } , - \frac { 3 } { 4 }$ 
C)   $- \frac { 1 } { 5 } , - \frac { 1 } { 4 }$ 
D)  $\frac { 4 } { 5 } , - \frac { 3 } { 4 }$

Question 12

Solve the equation.
-$x ^ { 3 } - x = - 7 x ^ { 2 } + 7$

Accepted Answer

A) - 7, 7 
B) 1, - 7, 7 
C) 49 
D) -1, 1, - 7 
A) - 7, 7 
B) 1, - 7, 7 
C) 49 
D) -1, 1, - 7

Question 13

Solve.
-The sum of a number and its square is 110. Find the number.

Accepted Answer

A) 10 or -11 
B) -10 or -11 
C) 10 or 11 
D) -10 or 11 
A) 10 or -11 
B) -10 or -11 
C) 10 or 11 
D) -10 or 11

Question 14

Solve the equation.
-$16 x ^ { 2 } = 25$

Accepted Answer

A)  $\frac { 5 } { 4 } , - \frac { 5 } { 4 }$ 
B)  $\frac { 5 } { 16 } , - \frac { 5 } { 16 }$ 
C)  $\frac { 5 } { 36 }$ 
D)  $\frac { 5 } { 6 }$ 
A)  $\frac { 5 } { 4 } , - \frac { 5 } { 4 }$ 
B)  $\frac { 5 } { 16 } , - \frac { 5 } { 16 }$ 
C)  $\frac { 5 } { 36 }$ 
D)  $\frac { 5 } { 6 }$

Question 15

Factor out the GCF from the polynomial.
-$20 x ^ { 4 } y + 28 x y ^ { 3 }$

Accepted Answer

A)  $x y \left( 20 x ^ { 3 } + 28 y ^ { 2 } \right)$ 
B)  $4 x \left( 5 x ^ { 3 } y + 7 y ^ { 3 } \right)$ 
C)  $4 x y \left( 5 x ^ { 3 } + 7 y ^ { 2 } \right)$ 
D)  $4 y \left( 5 x ^ { 4 } + 7 x y ^ { 2 } \right)$ 
A)  $x y \left( 20 x ^ { 3 } + 28 y ^ { 2 } \right)$ 
B)  $4 x \left( 5 x ^ { 3 } y + 7 y ^ { 3 } \right)$ 
C)  $4 x y \left( 5 x ^ { 3 } + 7 y ^ { 2 } \right)$ 
D)  $4 y \left( 5 x ^ { 4 } + 7 x y ^ { 2 } \right)$

Question 16

Factor the trinomial completely.
-$3 a ^ { 2 } b ^ { 2 } + 9 a b + 1$

Accepted Answer

A) 3(ab + 1)(ab + 3) 
B)  $3 \left( a ^ { 2 } b ^ { 2 } + 3 a b + 1 \right)$ 
C) (3ab + 1)(ab + 3) 
D) prime 
A) 3(ab + 1)(ab + 3) 
B)  $3 \left( a ^ { 2 } b ^ { 2 } + 3 a b + 1 \right)$ 
C) (3ab + 1)(ab + 3) 
D) prime

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

A)  $( 11 - x y ) ^ { 2 }$ 
B)  $( 11 + x y ) ^ { 2 }$ 
C) (11 - xy)(11 + xy) 
D) prime 
A)  $( 11 - x y ) ^ { 2 }$ 
B)  $( 11 + x y ) ^ { 2 }$ 
C) (11 - xy)(11 + xy) 
D) prime

Question 19

Solve the equation.
-$3 x ^ { 2 } - 18 x + 24 = 0$

Accepted Answer

A) -2, -4 
B) 3, 2, 4 
C) 0, 2, 4 
D) 2, 4 
A) -2, -4 
B) 3, 2, 4 
C) 0, 2, 4 
D) 2, 4

Question 20

Fill in the blank with one of the words or phrases listed below.
 
-The pythagorean theorem states thatythagorean theorem states that (l $( \operatorname { leg } ) ^ { 2 } + ( \operatorname { leg } ) ^ { 2 } = (\_\_\_\_)^2$

Accepted Answer

A) hypotenuse 
B) greatest common factor 
C) quadratic equation 
D) leg 
A) hypotenuse 
B) greatest common factor 
C) quadratic equation 
D) leg

Factor the trinomial completely. - $6 a ^ { 2 } - 7 a b - 3 b ^ { 2 }$

Solve the equation. -15 $15 d ^ { 2 } - 2 d = 0$

Represent the given condition using a single variable, x. -Three consecutive odd integers

Factor a -1 from the polynomial. -6a - b - 5

Solve the equation. -(4y + 5)(7y + 6)= 0

Factor the binomial completely. - $75 x ^ { 2 } y - 108 y$

Find the GCF for the list. - $x ^ { 6 } y ^ { 8 } , x ^ { 5 } y ^ { 7 } , x y ^ { 8 } , x ^ { 2 } y ^ { 6 }$

Factor the four-term polynomial by grouping. -6x - 66 + xy - 11y

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $4 t ^ { 2 } + t - 5$

Find the GCF for the list. - $10 \mathrm {~m} ^ { 4 } , 40 \mathrm {~m} ^ { 9 } , 100 \mathrm {~m} ^ { 5 }$

Solve the equation. - $20 y ^ { 2 } + 31 y + 12 = 0$

Solve the equation. - $x ^ { 3 } - x = - 7 x ^ { 2 } + 7$

Solve. -The sum of a number and its square is 110. Find the number.

Solve the equation. - $16 x ^ { 2 } = 25$

Factor out the GCF from the polynomial. - $20 x ^ { 4 } y + 28 x y ^ { 3 }$

Factor the trinomial completely. - $3 a ^ { 2 } b ^ { 2 } + 9 a b + 1$

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

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

Solve the equation. - $3 x ^ { 2 } - 18 x + 24 = 0$

The Whole Numbers

Multiplying and Dividing Fractions

Adding and Subtracting Fractions

Decimals

Ratio, Proportion, and Percent

Geometry

Statistics and Probability

Real Numbers and Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphing Equations and Inequalities

Systems of Equations

Exponents and Polynomials

Rational Expressions

Roots and Radicals

Quadratic Equations and Nonlinear Graphs

Algebraic Equations and Inequalities

Filters

Exam 13: Factoring Polynomials

Factor the trinomial completely. - 6a2−7ab−3b26 a ^ { 2 } - 7 a b - 3 b ^ { 2 }6a2−7ab−3b2

Solve the equation. -15 15d2−2d=015 d ^ { 2 } - 2 d = 015d2−2d=0