Question 1

Decide if the expression is factored
-$8 m-9 m^{2}$

Accepted Answer

A) True 
 B)False

Question 2

Factor the trinomial completely.
-$x^{2}+3 x y-154 y^{2}$

Accepted Answer

A)  Prime 
B)  $(x-14 y)(x+y)$ 
C)  $(x-14 y)(x+11 y)$ 
D)  $(x+14 y)(x-11 y)$ 
A)  Prime 
B)  $(x-14 y)(x+y)$ 
C)  $(x-14 y)(x+11 y)$ 
D)  $(x+14 y)(x-11 y)$

Question 3

A triangular garden has an area of 90 square feet. Its height is 3 feet more than its base. Find the measure of the base.

Accepted Answer

A)  9 feet 
B)  15 feet 
C)  24 feet 
D)  12 feet 
A)  9 feet 
B)  15 feet 
C)  24 feet 
D)  12 feet

Question 4

Solve the equation
-$16 y^{2}=(2 y-3)^{2}$

Accepted Answer

A)  $\left\{-\frac{3}{2}\right\}$ 
B)  $\left\{-\frac{1}{2}, 4\right\}$ 
C)  $\left\{\frac{3}{2},-\frac{3}{2}\right\}$ 
D)  $\left\{-\frac{3}{2}, \frac{1}{2}\right\}$ 
A)  $\left\{-\frac{3}{2}\right\}$ 
B)  $\left\{-\frac{1}{2}, 4\right\}$ 
C)  $\left\{\frac{3}{2},-\frac{3}{2}\right\}$ 
D)  $\left\{-\frac{3}{2}, \frac{1}{2}\right\}$

Question 5

$8 x^{2} y^{5}-4 x^{2} y^{3}-16 x^{6} y^{3}$

Accepted Answer

A)  $4 x^{2} y^{3}\left(4 y^{2}-x y-12 x^{4}\right)$ 
B)  $4 x^{2} y^{3}\left(2 y^{2}-1-4 x^{4}\right)$ 
C)  $4 x^{2} y^{3}\left(2 y^{2}-4 x^{4}\right)$ 
D)  $x^{2} y^{3}\left(8 y^{2}-4-16 x^{4}\right)$ 
A)  $4 x^{2} y^{3}\left(4 y^{2}-x y-12 x^{4}\right)$ 
B)  $4 x^{2} y^{3}\left(2 y^{2}-1-4 x^{4}\right)$ 
C)  $4 x^{2} y^{3}\left(2 y^{2}-4 x^{4}\right)$ 
D)  $x^{2} y^{3}\left(8 y^{2}-4-16 x^{4}\right)$

Question 6

$y^{3}-216$

Accepted Answer

A)  $(y-6)(y+6)^{2}$ 
B)  $(y+6)\left(y^{2}-6 y-36\right)$ 
C)  $(y-6)\left(y^{2}+6 y+36\right)$ 
D)  $(y-6)^{3}$ 
A)  $(y-6)(y+6)^{2}$ 
B)  $(y+6)\left(y^{2}-6 y-36\right)$ 
C)  $(y-6)\left(y^{2}+6 y+36\right)$ 
D)  $(y-6)^{3}$

Question 7

Factor the trinomial completely.
-$20 y^{2}+27 y+9$

Accepted Answer

A)  $(20 y+3)(y+3)$ 
B)  $(20 y+1)(y-9)$ 
C)  $(4 y+3)(5 y+3)$ 
D)  $(4 y-3)(5 y-3)$ 
A)  $(20 y+3)(y+3)$ 
B)  $(20 y+1)(y-9)$ 
C)  $(4 y+3)(5 y+3)$ 
D)  $(4 y-3)(5 y-3)$

Question 8

Factor the polynomial completely
-$27 y^{12}+8$

Accepted Answer

A)  $27 y^{12}+9$ 
B)  $\left(3 y^{4}+2\right)^{3}$ 
C)  $\left(9 y^{4}-4\right)\left(3 y^{4}+2\right)$ 
D)  $\left(3 y^{4}+2\right)\left(9 y^{8}-6 y^{4}+4\right)$ 
A)  $27 y^{12}+9$ 
B)  $\left(3 y^{4}+2\right)^{3}$ 
C)  $\left(9 y^{4}-4\right)\left(3 y^{4}+2\right)$ 
D)  $\left(3 y^{4}+2\right)\left(9 y^{8}-6 y^{4}+4\right)$

Question 9

Find all solutions by factoring.
-$x^{2}+7 x-30=0$

Accepted Answer

A)  $\{-10,3\}$ 
B)  $\{3,10\}$ 
C)  $\{-3,10\}$ 
D)  $\{-10,-3\}$ 
A)  $\{-10,3\}$ 
B)  $\{3,10\}$ 
C)  $\{-3,10\}$ 
D)  $\{-10,-3\}$

Question 10

A ball is projected upward from ground level. After $t$ seconds, its height in feet is a function defined by $f(t)=-16 t^{2}+64 t$. After how many seconds will it reach a height of $48 \mathrm{ft}$ ?

Accepted Answer

A)  $1.5 \mathrm{sec}$ and $3.5 \mathrm{sec}$ 
B)  $1 \mathrm{sec}$ and $3 \mathrm{sec}$ 
C)  The ball never reaches a height of 48 feet. 
D)  $1 \mathrm{sec}$ 
A)  $1.5 \mathrm{sec}$ and $3.5 \mathrm{sec}$ 
B)  $1 \mathrm{sec}$ and $3 \mathrm{sec}$ 
C)  The ball never reaches a height of 48 feet. 
D)  $1 \mathrm{sec}$

Question 11

Factor the polynomial completely
-$q^{4}-q^{3}-q+1$

Accepted Answer

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

Question 12

Solve the equation
-$3(4 m+1)^{2}=8(4 m+1)+16$

Accepted Answer

A)  $\left\{\frac{5}{4},-\frac{1}{12}\right\}$ 
B)  $\left\{\frac{1}{4},-\frac{7}{4}\right\}$ 
C)  $\left\{\frac{3}{4},-\frac{7}{12}\right\}$ 
D)  $\left\{-\frac{4}{3}, 4\right\}$ 
A)  $\left\{\frac{5}{4},-\frac{1}{12}\right\}$ 
B)  $\left\{\frac{1}{4},-\frac{7}{4}\right\}$ 
C)  $\left\{\frac{3}{4},-\frac{7}{12}\right\}$ 
D)  $\left\{-\frac{4}{3}, 4\right\}$

Question 13

Factor the trinomial completely.
-$88 m^{2}+153 m n+44 n^{2}$

Accepted Answer

A)  $\left(8 m+11 n^{2}\right)(11 m+4)$ 
B)  $(8 m-11 n)(11 m-4 n)$ 
C)  $(8 m+11 n)(11 m+4 n)$ 
D)  $(8 m+4 n)(11 m+11 n)$ 
A)  $\left(8 m+11 n^{2}\right)(11 m+4)$ 
B)  $(8 m-11 n)(11 m-4 n)$ 
C)  $(8 m+11 n)(11 m+4 n)$ 
D)  $(8 m+4 n)(11 m+11 n)$

Question 14

Factor by grouping.
-$x^{2}+5 x+9 x+45$

Accepted Answer

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

Question 15

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

Accepted Answer

A)  $(5 x+3)(5 x-3)$ 
B)  $(25 x+1)(x-9)$ 
C)  $(5 x-3)^{2}$ 
D)  $(5 x+3)^{2}$ 
A)  $(5 x+3)(5 x-3)$ 
B)  $(25 x+1)(x-9)$ 
C)  $(5 x-3)^{2}$ 
D)  $(5 x+3)^{2}$

Question 16

Factor the polynomial completely
-$x^{2}+4 x y-12 y^{2}$

Accepted Answer

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

Question 17

$-2 x^{2}-x+55$

Accepted Answer

A)  $-(2 x+11)(x-5)$ 
B)  cannot be factored 
C)  $(-2 x+9)(x+5)$ 
D)  $-(2 x+9)(x+5)$ 
A)  $-(2 x+11)(x-5)$ 
B)  cannot be factored 
C)  $(-2 x+9)(x+5)$ 
D)  $-(2 x+9)(x+5)$

Question 18

Factor the polynomial completely
-$u^{2}-3 u v-10 v^{2}$

Accepted Answer

A)  $(u+2 v)(u-5 v)$ 
B)  $(u-2 v)(u+v)$ 
C)  $(u-2 v)(u+5 v)$ 
D)  $(u-v)(u+5 v)$ 
A)  $(u+2 v)(u-5 v)$ 
B)  $(u-2 v)(u+v)$ 
C)  $(u-2 v)(u+5 v)$ 
D)  $(u-v)(u+5 v)$

Question 19

Factor the polynomial completely
-$8 a^{3}-27 b^{3}$

Accepted Answer

A)  $(2 a-3 b)\left(4 a^{2}+9 b^{2}\right)$ 
B)  $(2 a-3 b)\left(4 a^{2}+6 a b+9 b^{2}\right)$ 
C)  $\left(2 a+3 b^{2}\right)\left(4 a^{2}-6 a b+9 b^{2}\right)$ 
D)  $(8 a-3 b)\left(a^{2}+6 a b+9 b^{2}\right)$ 
A)  $(2 a-3 b)\left(4 a^{2}+9 b^{2}\right)$ 
B)  $(2 a-3 b)\left(4 a^{2}+6 a b+9 b^{2}\right)$ 
C)  $\left(2 a+3 b^{2}\right)\left(4 a^{2}-6 a b+9 b^{2}\right)$ 
D)  $(8 a-3 b)\left(a^{2}+6 a b+9 b^{2}\right)$

Question 20

Factor out the variable that is raised to the smaller exponent
-$7 x^{-8}+x^{-2}$

Accepted Answer

A)  $x^{-8}\left(7-x^{6}\right)$ 
B)  $x^{-8}\left(7-x^{-6}\right)$ 
C)  $x^{-8}\left(7+x^{6}\right)$ 
D)  $x^{-8}\left(7+x^{-6}\right)$ 
A)  $x^{-8}\left(7-x^{6}\right)$ 
B)  $x^{-8}\left(7-x^{-6}\right)$ 
C)  $x^{-8}\left(7+x^{6}\right)$ 
D)  $x^{-8}\left(7+x^{-6}\right)$

Decide if the expression is factored - $8 m-9 m^{2}$

Factor the trinomial completely. - $x^{2}+3 x y-154 y^{2}$

A triangular garden has an area of 90 square feet. Its height is 3 feet more than its base. Find the measure of the base.

Solve the equation - $16 y^{2}=(2 y-3)^{2}$

$8 x^{2} y^{5}-4 x^{2} y^{3}-16 x^{6} y^{3}$

$y^{3}-216$

Factor the trinomial completely. - $20 y^{2}+27 y+9$

Factor the polynomial completely - $27 y^{12}+8$

Find all solutions by factoring. - $x^{2}+7 x-30=0$

A ball is projected upward from ground level. After $t$ seconds, its height in feet is a function defined by $f(t)=-16 t^{2}+64 t$ . After how many seconds will it reach a height of $48 \mathrm{ft}$ ?

Factor the polynomial completely - $q^{4}-q^{3}-q+1$

Solve the equation - $3(4 m+1)^{2}=8(4 m+1)+16$

Factor the trinomial completely. - $88 m^{2}+153 m n+44 n^{2}$

Factor by grouping. - $x^{2}+5 x+9 x+45$

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

Factor the polynomial completely - $x^{2}+4 x y-12 y^{2}$

$-2 x^{2}-x+55$

Factor the polynomial completely - $u^{2}-3 u v-10 v^{2}$

Factor the polynomial completely - $8 a^{3}-27 b^{3}$

Factor out the variable that is raised to the smaller exponent - $7 x^{-8}+x^{-2}$

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

Decide if the expression is factored - 8m−9m28 m-9 m^{2}8m−9m2

Factor the trinomial completely. - x2+3xy−154y2x^{2}+3 x y-154 y^{2}x2+3xy−154y2

A triangular garden has an area of 90 square feet. Its height is 3 feet more than its base. Find the measure of the base.

Solve the equation - 16y2=(2y−3)216 y^{2}=(2 y-3)^{2}16y2=(2y−3)2

8x2y5−4x2y3−16x6y38 x^{2} y^{5}-4 x^{2} y^{3}-16 x^{6} y^{3}8x2y5−4x2y3−16x6y3

y3−216y^{3}-216y3−216

Factor the trinomial completely. - 20y2+27y+920 y^{2}+27 y+920y2+27y+9

Factor the polynomial completely - 27y12+827 y^{12}+827y12+8

Find all solutions by factoring. - x2+7x−30=0x^{2}+7 x-30=0x2+7x−30=0

A ball is projected upward from ground level. After ttt seconds, its height in feet is a function defined by f(t)=−16t2+64tf(t)=-16 t^{2}+64 tf(t)=−16t2+64t . After how many seconds will it reach a height of 48ft48 \mathrm{ft}48ft ?

Factor the polynomial completely - q4−q3−q+1q^{4}-q^{3}-q+1q4−q3−q+1

Solve the equation - 3(4m+1)2=8(4m+1)+163(4 m+1)^{2}=8(4 m+1)+163(4m+1)2=8(4m+1)+16

Factor the trinomial completely. - 88m2+153mn+44n288 m^{2}+153 m n+44 n^{2}88m2+153mn+44n2

Factor by grouping. - x2+5x+9x+45x^{2}+5 x+9 x+45x2+5x+9x+45

Factor the polynomial completely - 25x2−925 x^{2}-925x2−9

Factor the polynomial completely - x2+4xy−12y2x^{2}+4 x y-12 y^{2}x2+4xy−12y2

−2x2−x+55-2 x^{2}-x+55−2x2−x+55

Factor the polynomial completely - u2−3uv−10v2u^{2}-3 u v-10 v^{2}u2−3uv−10v2

Factor the polynomial completely - 8a3−27b38 a^{3}-27 b^{3}8a3−27b3

Factor out the variable that is raised to the smaller exponent - 7x−8+x−27 x^{-8}+x^{-2}7x−8+x−2

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

Decide if the expression is factored - $8 m-9 m^{2}$

Factor the trinomial completely. - $x^{2}+3 x y-154 y^{2}$

Solve the equation - $16 y^{2}=(2 y-3)^{2}$

$8 x^{2} y^{5}-4 x^{2} y^{3}-16 x^{6} y^{3}$

$y^{3}-216$

Factor the trinomial completely. - $20 y^{2}+27 y+9$

Factor the polynomial completely - $27 y^{12}+8$

Find all solutions by factoring. - $x^{2}+7 x-30=0$

A ball is projected upward from ground level. After $t$ seconds, its height in feet is a function defined by $f(t)=-16 t^{2}+64 t$ . After how many seconds will it reach a height of $48 \mathrm{ft}$ ?

Factor the polynomial completely - $q^{4}-q^{3}-q+1$

Solve the equation - $3(4 m+1)^{2}=8(4 m+1)+16$

Factor the trinomial completely. - $88 m^{2}+153 m n+44 n^{2}$

Factor by grouping. - $x^{2}+5 x+9 x+45$

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

Factor the polynomial completely - $x^{2}+4 x y-12 y^{2}$

$-2 x^{2}-x+55$

Factor the polynomial completely - $u^{2}-3 u v-10 v^{2}$

Factor the polynomial completely - $8 a^{3}-27 b^{3}$

Factor out the variable that is raised to the smaller exponent - $7 x^{-8}+x^{-2}$