Question 1

$4 x^{2}-3 x=0$

Accepted Answer

A)  $\left\{\frac{3}{4}\right\}$ 
B)  $\left\{0, \frac{3}{4}\right\}$ 
C)  $\{0,3\}$ 
D)  $\left\{1, \frac{4}{3}\right\}$ 
A)  $\left\{\frac{3}{4}\right\}$ 
B)  $\left\{0, \frac{3}{4}\right\}$ 
C)  $\{0,3\}$ 
D)  $\left\{1, \frac{4}{3}\right\}$

Question 2

Factor the polynomial completely
-$9 y^{4}-4$

Accepted Answer

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

Question 3

Factor the trinomial completely.
-$3 x^{2}-9 x y-12 y^{2}$

Accepted Answer

A)  $(3 x-3 y)(x+4 y)$ 
B)  $3(x+y)(x-4 y)$ 
C)  $3(x-y)(x+4 y)$ 
D)  $(x-y)(3 x+9 y)$ 
A)  $(3 x-3 y)(x+4 y)$ 
B)  $3(x+y)(x-4 y)$ 
C)  $3(x-y)(x+4 y)$ 
D)  $(x-y)(3 x+9 y)$

Question 4

Factor the polynomial completely
-$49 a^{2}-144 q^{4}$

Accepted Answer

A)  $\left(7 a-12 q^{2}\right)^{2}$ 
B)  $49 a^{2}-144 q^{4}$ 
C)  $\left(7 a-12 q^{2}\right)\left(7 a-12 q^{2}\right)$ 
D)  $\left(7 a+12 q^{2}\right)\left(7 a-12 q^{2}\right)$ 
A)  $\left(7 a-12 q^{2}\right)^{2}$ 
B)  $49 a^{2}-144 q^{4}$ 
C)  $\left(7 a-12 q^{2}\right)\left(7 a-12 q^{2}\right)$ 
D)  $\left(7 a+12 q^{2}\right)\left(7 a-12 q^{2}\right)$

Question 5

Factor the polynomial completely
-$t^{3}+125$

Accepted Answer

A)  $(\mathrm{t}-125)\left(\mathrm{t}^{2}-1\right)$ 
B)  $(t-5)\left(t^{2}+5 t+25\right)$ 
C)  $(t+5)\left(t^{2}-5 t+25\right)$ 
D)  $(t+5)\left(t^{2}+25\right)$ 
A)  $(\mathrm{t}-125)\left(\mathrm{t}^{2}-1\right)$ 
B)  $(t-5)\left(t^{2}+5 t+25\right)$ 
C)  $(t+5)\left(t^{2}-5 t+25\right)$ 
D)  $(t+5)\left(t^{2}+25\right)$

Question 6

Factor the polynomial completely
-$50 a^{4} b-72 b^{3}$

Accepted Answer

A)  $2 b\left(5 a^{2}+6 b\right)\left(5 a^{2}-6 b\right)$ 
B)  $2 b(5 a+6 b)^{2}$ 
C)  $2 b(5 a-6 b)^{2}$ 
D)  $(10 a+12 b)\left(5 a b-6 b^{2}\right)$ 
A)  $2 b\left(5 a^{2}+6 b\right)\left(5 a^{2}-6 b\right)$ 
B)  $2 b(5 a+6 b)^{2}$ 
C)  $2 b(5 a-6 b)^{2}$ 
D)  $(10 a+12 b)\left(5 a b-6 b^{2}\right)$

Question 7

Factor out the variable that is raised to the smaller exponent
-$-5 x^{-2}+x^{2}$

Accepted Answer

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

Question 8

Factor the polynomial completely
-$75 a^{4} b-147 b^{3}$

Accepted Answer

A)  $3 b(5 a+7 b)^{2}$ 
B)  $3 b\left(5 a^{2}+7 b\right)\left(5 a^{2}-7 b\right)$ 
C)  $(15 a+21 b)\left(5 a b-7 b^{2}\right)$ 
D)  $3 b(5 a-7 b)^{2}$ 
A)  $3 b(5 a+7 b)^{2}$ 
B)  $3 b\left(5 a^{2}+7 b\right)\left(5 a^{2}-7 b\right)$ 
C)  $(15 a+21 b)\left(5 a b-7 b^{2}\right)$ 
D)  $3 b(5 a-7 b)^{2}$

Question 9

Factor the polynomial completely
-$9 x^{2}+25$

Accepted Answer

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

Question 10

Factor by grouping.
-$3-3 t+t^{2}-t^{3}$

Accepted Answer

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

Question 11

Factor the trinomial completely.
-$2 x^{2}-12 x+16$

Accepted Answer

A)  $(2 x-4)(x-4)$ 
B)  $2(x-2)(x-4)$ 
C)  $2(x-8)(x+1)$ 
D)  $(x-2)(2 x-8)$ 
A)  $(2 x-4)(x-4)$ 
B)  $2(x-2)(x-4)$ 
C)  $2(x-8)(x+1)$ 
D)  $(x-2)(2 x-8)$

Question 12

$6 k^{4}-k^{2}-117$

Accepted Answer

A)  $\left(2 \mathrm{k}^{2}-9\right)\left(3 \mathrm{k}^{2}+13\right)$ 
B)  $\left(6 k^{2}+9\right)\left(k^{2}-13\right)$ 
C)  $\left.2 k^{2}+9\right)\left(3 k^{2}-13\right)$ 
D)  $(2 k+9)(2 k-9)(2 k+13)$ 
A)  $\left(2 \mathrm{k}^{2}-9\right)\left(3 \mathrm{k}^{2}+13\right)$ 
B)  $\left(6 k^{2}+9\right)\left(k^{2}-13\right)$ 
C)  $\left.2 k^{2}+9\right)\left(3 k^{2}-13\right)$ 
D)  $(2 k+9)(2 k-9)(2 k+13)$

Question 13

Factor the trinomial completely.
-$a^{2}(a+b)^{2}-a b(a+b)^{2}-30 b^{2}(a+b)^{2}$

Accepted Answer

A)  $(a+b)^{2}(a-6)(a+5)$ 
B)  $(a+b)^{2}(a-5 b)(a+6 b)$ 
C)  $(a+b)^{2}(a-6 b)(a+5 b)$ 
D)  $(a-6 b)(a+5 b)(a+b)$ 
A)  $(a+b)^{2}(a-6)(a+5)$ 
B)  $(a+b)^{2}(a-5 b)(a+6 b)$ 
C)  $(a+b)^{2}(a-6 b)(a+5 b)$ 
D)  $(a-6 b)(a+5 b)(a+b)$

Question 14

The printed matter on a 14 by 20 centimeter page of a book must cover 160 square centimeters. If all margins are to be the same width, how wide should they be?

Accepted Answer

A)  $2 \mathrm{~cm}$ 
B)  $1 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  $4 \mathrm{~cm}$ 
A)  $2 \mathrm{~cm}$ 
B)  $1 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  $4 \mathrm{~cm}$

Question 15

Factor the trinomial completely.
-$6 x^{2}-21 x-12$

Accepted Answer

A)  $(2 x-1)(3 x+12)$ 
B)  $3(2 x+1)(x-4)$ 
C)  $(6 x-3)(x+4)$ 
D)  $3(2 x-1)(x+4)$ 
A)  $(2 x-1)(3 x+12)$ 
B)  $3(2 x+1)(x-4)$ 
C)  $(6 x-3)(x+4)$ 
D)  $3(2 x-1)(x+4)$

Question 16

Solve the equation
-$3 x^{3}+14 x^{2}+15 x=0$

Accepted Answer

A)  $\left\{3, \frac{5}{3}\right\}$ 
B)  $\left\{-3,-\frac{5}{3}, 0\right\}$ 
C)  $\left\{-3,-\frac{5}{3}\right\}$ 
D)  $\left\{0,3, \frac{5}{3}\right\}$ 
A)  $\left\{3, \frac{5}{3}\right\}$ 
B)  $\left\{-3,-\frac{5}{3}, 0\right\}$ 
C)  $\left\{-3,-\frac{5}{3}\right\}$ 
D)  $\left\{0,3, \frac{5}{3}\right\}$

Question 17

Decide if the expression is factored
-$(7 x+5 y)(7 x-5 y)$

Accepted Answer

A) True 
 B)False

Question 18

Factor the polynomial completely
-$25 x^{2}-10 x+1-y^{2}$

Accepted Answer

A)  Prime 
B)  $(5 x-1+y)(5 x+1-y)$ 
C)  $(5 x-1+y)(5 x-1-y)$ 
D)  $(5 x+1+y)(5 x+1-y)$ 
A)  Prime 
B)  $(5 x-1+y)(5 x+1-y)$ 
C)  $(5 x-1+y)(5 x-1-y)$ 
D)  $(5 x+1+y)(5 x+1-y)$

Question 19

Factor out the variable that is raised to the smaller exponent
-$x^{-9}-7 x^{-4}$

Accepted Answer

A)  $x^{-9}\left(1-7 x^{5}\right)$ 
B)  $x^{-9}\left(1+7 x^{-5}\right)$ 
C)  $x^{-9}\left(1+7 x^{5}\right)$ 
D)  $x^{-9}\left(-1+7 x^{5}\right)$ 
A)  $x^{-9}\left(1-7 x^{5}\right)$ 
B)  $x^{-9}\left(1+7 x^{-5}\right)$ 
C)  $x^{-9}\left(1+7 x^{5}\right)$ 
D)  $x^{-9}\left(-1+7 x^{5}\right)$

Question 20

Factor the polynomial completely
-$x^{2}-y^{2}+8 y-16$

Accepted Answer

A)  $(1-4)(x+y)(x-y)$ 
B)  $(x+y-4)(x-y-4)$ 
C)  $(\mathrm{x}-\mathrm{y}-4)(\mathrm{x}-\mathrm{y}+4)$ 
D)  $(x+y-4)(x-y+4)$ 
A)  $(1-4)(x+y)(x-y)$ 
B)  $(x+y-4)(x-y-4)$ 
C)  $(\mathrm{x}-\mathrm{y}-4)(\mathrm{x}-\mathrm{y}+4)$ 
D)  $(x+y-4)(x-y+4)$

$4 x^{2}-3 x=0$

Factor the polynomial completely - $9 y^{4}-4$

Factor the trinomial completely. - $3 x^{2}-9 x y-12 y^{2}$

Factor the polynomial completely - $49 a^{2}-144 q^{4}$

Factor the polynomial completely - $t^{3}+125$

Factor the polynomial completely - $50 a^{4} b-72 b^{3}$

Factor out the variable that is raised to the smaller exponent - $-5 x^{-2}+x^{2}$

Factor the polynomial completely - $75 a^{4} b-147 b^{3}$

Factor the polynomial completely - $9 x^{2}+25$

Factor by grouping. - $3-3 t+t^{2}-t^{3}$

Factor the trinomial completely. - $2 x^{2}-12 x+16$

$6 k^{4}-k^{2}-117$

Factor the trinomial completely. - $a^{2}(a+b)^{2}-a b(a+b)^{2}-30 b^{2}(a+b)^{2}$

The printed matter on a 14 by 20 centimeter page of a book must cover 160 square centimeters. If all margins are to be the same width, how wide should they be?

Factor the trinomial completely. - $6 x^{2}-21 x-12$

Solve the equation - $3 x^{3}+14 x^{2}+15 x=0$

Decide if the expression is factored - $(7 x+5 y)(7 x-5 y)$

Factor the polynomial completely - $25 x^{2}-10 x+1-y^{2}$

Factor out the variable that is raised to the smaller exponent - $x^{-9}-7 x^{-4}$

Factor the polynomial completely - $x^{2}-y^{2}+8 y-16$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 6: Factoring

4x2−3x=04 x^{2}-3 x=04x2−3x=0

Factor the polynomial completely - 9y4−49 y^{4}-49y4−4

Factor the trinomial completely. - 3x2−9xy−12y23 x^{2}-9 x y-12 y^{2}3x2−9xy−12y2

Factor the polynomial completely - 49a2−144q449 a^{2}-144 q^{4}49a2−144q4

Factor the polynomial completely - t3+125t^{3}+125t3+125

Factor the polynomial completely - 50a4b−72b350 a^{4} b-72 b^{3}50a4b−72b3

Factor out the variable that is raised to the smaller exponent - −5x−2+x2-5 x^{-2}+x^{2}−5x−2+x2

Factor the polynomial completely - 75a4b−147b375 a^{4} b-147 b^{3}75a4b−147b3

Factor the polynomial completely - 9x2+259 x^{2}+259x2+25

Factor by grouping. - 3−3t+t2−t33-3 t+t^{2}-t^{3}3−3t+t2−t3

Factor the trinomial completely. - 2x2−12x+162 x^{2}-12 x+162x2−12x+16

6k4−k2−1176 k^{4}-k^{2}-1176k4−k2−117

Factor the trinomial completely. - a2(a+b)2−ab(a+b)2−30b2(a+b)2a^{2}(a+b)^{2}-a b(a+b)^{2}-30 b^{2}(a+b)^{2}a2(a+b)2−ab(a+b)2−30b2(a+b)2

The printed matter on a 14 by 20 centimeter page of a book must cover 160 square centimeters. If all margins are to be the same width, how wide should they be?

Factor the trinomial completely. - 6x2−21x−126 x^{2}-21 x-126x2−21x−12

Solve the equation - 3x3+14x2+15x=03 x^{3}+14 x^{2}+15 x=03x3+14x2+15x=0

Decide if the expression is factored - (7x+5y)(7x−5y)(7 x+5 y)(7 x-5 y)(7x+5y)(7x−5y)

Factor the polynomial completely - 25x2−10x+1−y225 x^{2}-10 x+1-y^{2}25x2−10x+1−y2

Factor out the variable that is raised to the smaller exponent - x−9−7x−4x^{-9}-7 x^{-4}x−9−7x−4

Factor the polynomial completely - x2−y2+8y−16x^{2}-y^{2}+8 y-16x2−y2+8y−16

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

$4 x^{2}-3 x=0$

Factor the polynomial completely - $9 y^{4}-4$

Factor the trinomial completely. - $3 x^{2}-9 x y-12 y^{2}$

Factor the polynomial completely - $49 a^{2}-144 q^{4}$

Factor the polynomial completely - $t^{3}+125$

Factor the polynomial completely - $50 a^{4} b-72 b^{3}$

Factor out the variable that is raised to the smaller exponent - $-5 x^{-2}+x^{2}$

Factor the polynomial completely - $75 a^{4} b-147 b^{3}$

Factor the polynomial completely - $9 x^{2}+25$

Factor by grouping. - $3-3 t+t^{2}-t^{3}$

Factor the trinomial completely. - $2 x^{2}-12 x+16$

$6 k^{4}-k^{2}-117$

Factor the trinomial completely. - $a^{2}(a+b)^{2}-a b(a+b)^{2}-30 b^{2}(a+b)^{2}$

Factor the trinomial completely. - $6 x^{2}-21 x-12$

Solve the equation - $3 x^{3}+14 x^{2}+15 x=0$

Decide if the expression is factored - $(7 x+5 y)(7 x-5 y)$

Factor the polynomial completely - $25 x^{2}-10 x+1-y^{2}$

Factor out the variable that is raised to the smaller exponent - $x^{-9}-7 x^{-4}$

Factor the polynomial completely - $x^{2}-y^{2}+8 y-16$