Question 1

Factor the polynomial completely
-$8 c^{3}+27$

Accepted Answer

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

Question 2

Solve the equation
-$3(a-1)^{2}+4=13(a-1)$

Accepted Answer

A)  $\left\{\frac{7}{3}, 2\right\}$ 
B)  $\left\{\frac{1}{3}, 4\right\}$ 
C)  $\left\{\frac{2}{3},-3\right\}$ 
D)  $\left\{\frac{4}{3}, 5\right\}$ 
A)  $\left\{\frac{7}{3}, 2\right\}$ 
B)  $\left\{\frac{1}{3}, 4\right\}$ 
C)  $\left\{\frac{2}{3},-3\right\}$ 
D)  $\left\{\frac{4}{3}, 5\right\}$

Question 3

Factor the polynomial completely
-$1250 a^{4}-875 a^{3}+270 a x^{3}-189 x^{3}$

Accepted Answer

A)  $\left(140 a^{2}-98 a+120 a x-84 x\right)\left(25 a^{2}+15 a x+25 x^{2}\right)$ 
B)  $125 a^{3}(10 a-7)+27 x^{3}(10 a-7)$ 
C)  $(5 a+3 x)(10 a-7)\left(25 a^{2}-15 a x+9 x^{2}\right)$ 
D)  $1250 a^{4}-875 a^{3}-270 a x^{3}+189 x^{3}$ 
A)  $\left(140 a^{2}-98 a+120 a x-84 x\right)\left(25 a^{2}+15 a x+25 x^{2}\right)$ 
B)  $125 a^{3}(10 a-7)+27 x^{3}(10 a-7)$ 
C)  $(5 a+3 x)(10 a-7)\left(25 a^{2}-15 a x+9 x^{2}\right)$ 
D)  $1250 a^{4}-875 a^{3}-270 a x^{3}+189 x^{3}$

Question 4

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

Accepted Answer

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

Question 5

Find all solutions by factoring.
-$(x-3)(x+2)=84$

Accepted Answer

A)  $\{82,3\}$ 
B)  $\{3,-2\}$ 
C)  $\{-9,10\}$ 
D)  $\{-2,87\}$ 
A)  $\{82,3\}$ 
B)  $\{3,-2\}$ 
C)  $\{-9,10\}$ 
D)  $\{-2,87\}$

Question 6

Find all solutions by factoring.
-$5 \mathrm{~m}^{2}-14 \mathrm{~m}=0$

Accepted Answer

A)  $\left\{\frac{14}{5}, 0\right\}$ 
B)  $\{0\}$ 
C)  $\left\{\frac{14}{5},-\frac{14}{5}\right\}$ 
D)  $\left\{-\frac{14}{5}, 0\right\}$ 
A)  $\left\{\frac{14}{5}, 0\right\}$ 
B)  $\{0\}$ 
C)  $\left\{\frac{14}{5},-\frac{14}{5}\right\}$ 
D)  $\left\{-\frac{14}{5}, 0\right\}$

Question 7

actor out the greatest common factor. Simplify the factors, if possible
-$20 w x-12 w y-16 w z$

Accepted Answer

A)  $4 w(5 x-3 y-4 z)$ 
B)  $20 w(x-12 y-16 z)$ 
C)  $4(5 w x-3 w y-4 w z)$ 
D)  $4 w(5 x-12 w y-16 w z)$ 
A)  $4 w(5 x-3 y-4 z)$ 
B)  $20 w(x-12 y-16 z)$ 
C)  $4(5 w x-3 w y-4 w z)$ 
D)  $4 w(5 x-12 w y-16 w z)$

Question 8

The area of the rectangle shown is given by the polynomial $20 x^{2}+37 x+8$, where the width is $4 x+$ 1. Express the length of the rectangle in terms of $x$.

Accepted Answer

A)  $20 x^{2}+33 x+7$ 
B)  $5 x^{2}+33 x+8$ 
C)  $5 x+8$ 
D)  $4 x+8$ 
A)  $20 x^{2}+33 x+7$ 
B)  $5 x^{2}+33 x+8$ 
C)  $5 x+8$ 
D)  $4 x+8$

Question 9

Factor out the variable that is raised to the smaller exponent
-$x^{-7}+6 x^{-2}$

Accepted Answer

A)  $x^{-7}\left(1+6 x^{5}\right)$ 
B)  $x^{-7}\left(1+6 x^{-5}\right)$ 
C)  $x^{-7}\left(6 x^{5}\right)$ 
D)  $x^{-7}\left(x+6 x^{5}\right)$ 
A)  $x^{-7}\left(1+6 x^{5}\right)$ 
B)  $x^{-7}\left(1+6 x^{-5}\right)$ 
C)  $x^{-7}\left(6 x^{5}\right)$ 
D)  $x^{-7}\left(x+6 x^{5}\right)$

Question 10

Factor the polynomial completely
-$1000 y^{3}-729$

Accepted Answer

A)  $(10 y-9)\left(100 y^{2}+90 y+81\right)$ 
B)  $(10 y+9)\left(100 y^{2}-90 y+81\right)$ 
C)  $(1000 y-9)\left(y^{2}+90 y+81\right)$ 
D)  $(10 y-9)\left(100 y^{2}+81\right)$ 
A)  $(10 y-9)\left(100 y^{2}+90 y+81\right)$ 
B)  $(10 y+9)\left(100 y^{2}-90 y+81\right)$ 
C)  $(1000 y-9)\left(y^{2}+90 y+81\right)$ 
D)  $(10 y-9)\left(100 y^{2}+81\right)$

Question 11

Factor the trinomial completely.
-$-x^{2}+2 x+8$

Accepted Answer

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

Question 12

A box with no top is to be constructed from a piece of cardboard whose width measures $x \mathrm{~cm}$ and whose length measures $3 \mathrm{~cm}$ more than its width. The box is to be formed by cutting squares that measure $1 \mathrm{~cm}$ on each side from the four corners, and then folding up the sides. If the volume of the box will be $130 \mathrm{~cm}^{3}$, what are the dimensions of the piece of cardboard?

Accepted Answer

A)  $15 \mathrm{~cm}$ by $12 \mathrm{~cm}$ 
B)  $23 \mathrm{~cm}$ by $16 \mathrm{~cm}$ 
C)  $18 \mathrm{~cm}$ by $15 \mathrm{~cm}$ 
D)  $19 \mathrm{~cm}$ by $16 \mathrm{~cm}$ 
A)  $15 \mathrm{~cm}$ by $12 \mathrm{~cm}$ 
B)  $23 \mathrm{~cm}$ by $16 \mathrm{~cm}$ 
C)  $18 \mathrm{~cm}$ by $15 \mathrm{~cm}$ 
D)  $19 \mathrm{~cm}$ by $16 \mathrm{~cm}$

Question 13

$9 \mathrm{k}^{2}-100 \mathrm{j}^{2}$

Accepted Answer

A)  $30(\mathrm{k}-\mathrm{j})(\mathrm{k}+\mathrm{j})$ 
B)  $(3 \mathrm{k}-10 \mathrm{j})^{2}$ 
C)  cannot be factored 
D)  $(3 \mathrm{k}-10 \mathrm{j})(3 \mathrm{k}+10 \mathrm{j})$ 
A)  $30(\mathrm{k}-\mathrm{j})(\mathrm{k}+\mathrm{j})$ 
B)  $(3 \mathrm{k}-10 \mathrm{j})^{2}$ 
C)  cannot be factored 
D)  $(3 \mathrm{k}-10 \mathrm{j})(3 \mathrm{k}+10 \mathrm{j})$

Question 14

Factor the trinomial completely.
-$15(\mathrm{p}+2)^{2}+14(\mathrm{p}+2)+3$

Accepted Answer

A)  $(3 p+9)(5 p+11)$ 
B)  $(3 p+1)(5 p+3)$ 
C)  $(3 p+3)(5 p+5)$ 
D)  $(3 p+7)(5 p+13)$ 
A)  $(3 p+9)(5 p+11)$ 
B)  $(3 p+1)(5 p+3)$ 
C)  $(3 p+3)(5 p+5)$ 
D)  $(3 p+7)(5 p+13)$

Question 15

Factor the polynomial completely
-$(x-y)^{3}-216$

Accepted Answer

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

Question 16

Factor the trinomial completely.
-$x^{2} y^{2}+12 x y+35$

Accepted Answer

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

Question 17

Factor the trinomial completely.
-$-x^{2}-2 x+63$

Accepted Answer

A)  $-(x-7)(x+9)$ 
B)  Prime 
C)  $-(x-7)(x-9)$ 
D)  $(x+7)(x-9)$ 
A)  $-(x-7)(x+9)$ 
B)  Prime 
C)  $-(x-7)(x-9)$ 
D)  $(x+7)(x-9)$

Question 18

Factor the trinomial completely.
-$-m^{2}+5 m+50$

Accepted Answer

A)  $(10-m)(m-5)$ 
B)  Prime 
C)  $(10-m)(m+5)$ 
D)  $(m+10)(m-5)$ 
A)  $(10-m)(m-5)$ 
B)  Prime 
C)  $(10-m)(m+5)$ 
D)  $(m+10)(m-5)$

Question 19

Which of the following equations is not in proper form for using the zero-factor property?
Explain.
$$\begin{aligned}
& 3 n(n-4)(n-5)=0 \
& a(a-6)-3(a-5)=0 \
& (z-3)(z-1)=0 \
& y(-3 y-1)=0
\end{aligned}$$

Accepted Answer

@#LAT-DLM&. The equation is no

Question 20

Solve the equation
-$3(p+4)^{2}-10(p+4)+3=0$

Accepted Answer

A)  $\left\{-\frac{11}{3},-1\right\}$ 
B)  $\left\{\frac{1}{3}, 3\right\}$ 
C)  $\{-3,-3\}$ 
D)  $\left\{-\frac{13}{3},-7\right\}$ 
A)  $\left\{-\frac{11}{3},-1\right\}$ 
B)  $\left\{\frac{1}{3}, 3\right\}$ 
C)  $\{-3,-3\}$ 
D)  $\left\{-\frac{13}{3},-7\right\}$

Factor the polynomial completely - $8 c^{3}+27$

Solve the equation - $3(a-1)^{2}+4=13(a-1)$

Factor the polynomial completely - $1250 a^{4}-875 a^{3}+270 a x^{3}-189 x^{3}$

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

Find all solutions by factoring. - $(x-3)(x+2)=84$

Find all solutions by factoring. - $5 \mathrm{~m}^{2}-14 \mathrm{~m}=0$

actor out the greatest common factor. Simplify the factors, if possible - $20 w x-12 w y-16 w z$

Factor out the variable that is raised to the smaller exponent - $x^{-7}+6 x^{-2}$

Factor the polynomial completely - $1000 y^{3}-729$

Factor the trinomial completely. - $-x^{2}+2 x+8$

$9 \mathrm{k}^{2}-100 \mathrm{j}^{2}$

Factor the trinomial completely. - $15(\mathrm{p}+2)^{2}+14(\mathrm{p}+2)+3$

Factor the polynomial completely - $(x-y)^{3}-216$

Factor the trinomial completely. - $x^{2} y^{2}+12 x y+35$

Factor the trinomial completely. - $-x^{2}-2 x+63$

Factor the trinomial completely. - $-m^{2}+5 m+50$

Which of the following equations is not in proper form for using the zero-factor property? Explain. 3n(n-4)(n-5)=0 a(a-6)-3(a-5)=0 (z-3)(z-1)=0 y(-3y-1)=0

Solve the equation - $3(p+4)^{2}-10(p+4)+3=0$

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

Factor the polynomial completely - 8c3+278 c^{3}+278c3+27

Solve the equation - 3(a−1)2+4=13(a−1)3(a-1)^{2}+4=13(a-1)3(a−1)2+4=13(a−1)

Factor the polynomial completely - 1250a4−875a3+270ax3−189x31250 a^{4}-875 a^{3}+270 a x^{3}-189 x^{3}1250a4−875a3+270ax3−189x3

Factor the polynomial - x2+8xy+16y2x^{2}+8 x y+16 y^{2}x2+8xy+16y2

Find all solutions by factoring. - (x−3)(x+2)=84(x-3)(x+2)=84(x−3)(x+2)=84

Find all solutions by factoring. - 5 m2−14 m=05 \mathrm{~m}^{2}-14 \mathrm{~m}=05 m2−14 m=0

actor out the greatest common factor. Simplify the factors, if possible - 20wx−12wy−16wz20 w x-12 w y-16 w z20wx−12wy−16wz

The area of the rectangle shown is given by the polynomial 20x2+37x+820 x^{2}+37 x+820x2+37x+8 , where the width is 4x+4 x+4x+ 1. Express the length of the rectangle in terms of xxx .

Factor out the variable that is raised to the smaller exponent - x−7+6x−2x^{-7}+6 x^{-2}x−7+6x−2

Factor the polynomial completely - 1000y3−7291000 y^{3}-7291000y3−729

Factor the trinomial completely. - −x2+2x+8-x^{2}+2 x+8−x2+2x+8

9k2−100j29 \mathrm{k}^{2}-100 \mathrm{j}^{2}9k2−100j2

Factor the trinomial completely. - 15(p+2)2+14(p+2)+315(\mathrm{p}+2)^{2}+14(\mathrm{p}+2)+315(p+2)2+14(p+2)+3

Factor the polynomial completely - (x−y)3−216(x-y)^{3}-216(x−y)3−216

Factor the trinomial completely. - x2y2+12xy+35x^{2} y^{2}+12 x y+35x2y2+12xy+35

Factor the trinomial completely. - −x2−2x+63-x^{2}-2 x+63−x2−2x+63

Factor the trinomial completely. - −m2+5m+50-m^{2}+5 m+50−m2+5m+50

Which of the following equations is not in proper form for using the zero-factor property? Explain. 3n(n-4)(n-5)=0 a(a-6)-3(a-5)=0 (z-3)(z-1)=0 y(-3y-1)=0

Solve the equation - 3(p+4)2−10(p+4)+3=03(p+4)^{2}-10(p+4)+3=03(p+4)2−10(p+4)+3=0

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

Factor the polynomial completely - $8 c^{3}+27$

Solve the equation - $3(a-1)^{2}+4=13(a-1)$

Factor the polynomial completely - $1250 a^{4}-875 a^{3}+270 a x^{3}-189 x^{3}$

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

Find all solutions by factoring. - $(x-3)(x+2)=84$

Find all solutions by factoring. - $5 \mathrm{~m}^{2}-14 \mathrm{~m}=0$

actor out the greatest common factor. Simplify the factors, if possible - $20 w x-12 w y-16 w z$

Factor out the variable that is raised to the smaller exponent - $x^{-7}+6 x^{-2}$

Factor the polynomial completely - $1000 y^{3}-729$

Factor the trinomial completely. - $-x^{2}+2 x+8$

$9 \mathrm{k}^{2}-100 \mathrm{j}^{2}$

Factor the trinomial completely. - $15(\mathrm{p}+2)^{2}+14(\mathrm{p}+2)+3$

Factor the polynomial completely - $(x-y)^{3}-216$

Factor the trinomial completely. - $x^{2} y^{2}+12 x y+35$

Factor the trinomial completely. - $-x^{2}-2 x+63$

Factor the trinomial completely. - $-m^{2}+5 m+50$

Solve the equation - $3(p+4)^{2}-10(p+4)+3=0$