Question 1

Factor the polynomial
-$9 x^{2}-6 x+1-y^{2}$

Accepted Answer

A)  $(3 x+1+y)(3 x+1-y)$ 
B)  $(3 x-1+y)(3 x-1-y)$ 
C)  Prime 
D)  $(3 x-1+y)(3 x+1-y)$ 
A)  $(3 x+1+y)(3 x+1-y)$ 
B)  $(3 x-1+y)(3 x-1-y)$ 
C)  Prime 
D)  $(3 x-1+y)(3 x+1-y)$

Question 2

Factor the polynomial completely
-$(m-n)^{2}-8(m-n)+16$

Accepted Answer

A)  $(m-n-4)^{2}$ 
B)  $(\mathrm{m}-\mathrm{n}-4)(\mathrm{m}-\mathrm{n}+4)$ 
C)  $(\mathrm{m}-\mathrm{n}-16)(\mathrm{m}-\mathrm{n})$ 
D)  Prime 
A)  $(m-n-4)^{2}$ 
B)  $(\mathrm{m}-\mathrm{n}-4)(\mathrm{m}-\mathrm{n}+4)$ 
C)  $(\mathrm{m}-\mathrm{n}-16)(\mathrm{m}-\mathrm{n})$ 
D)  Prime

Question 3

Factor the trinomial completely.
-$60 z^{6}-16 z^{4}-16 z^{2}$

Accepted Answer

A)  $\left(12 z^{3}-8\right)\left(5 z^{3}+2\right)$ 
B)  $4 z^{2}\left(3 z^{2}-2\right)\left(5 z^{2}+2\right)$ 
C)  $4 z^{2}\left(5 z^{2}-2\right)\left(3 z^{2}+2\right)$ 
D)  $4\left(3 z^{4}-2\right)\left(5 z^{2}+2\right)$ 
A)  $\left(12 z^{3}-8\right)\left(5 z^{3}+2\right)$ 
B)  $4 z^{2}\left(3 z^{2}-2\right)\left(5 z^{2}+2\right)$ 
C)  $4 z^{2}\left(5 z^{2}-2\right)\left(3 z^{2}+2\right)$ 
D)  $4\left(3 z^{4}-2\right)\left(5 z^{2}+2\right)$

Question 4

Find all solutions by factoring.
-$9 x^{2}=9 x$

Accepted Answer

A)  $\{1\}$ 
B)  $\{0,1\}$ 
C)  $\{9,-9\}$ 
D)  $\{0,9\}$ 
A)  $\{1\}$ 
B)  $\{0,1\}$ 
C)  $\{9,-9\}$ 
D)  $\{0,9\}$

Question 5

The area of a square is given by the polynomial $25 x^{2}+30 x y+9 y^{2}$. Find the length of a side of the square in terms of $x$ and $y$.

Accepted Answer

A)  $25 x^{2}+31 y$ 
B)  $25 x^{2}+9 y^{2}$ 
C)  $25 x^{2}+25 x y+6 y^{2}$ 
D)  $5 x+3 y$ 
A)  $25 x^{2}+31 y$ 
B)  $25 x^{2}+9 y^{2}$ 
C)  $25 x^{2}+25 x y+6 y^{2}$ 
D)  $5 x+3 y$

Question 6

Factor the trinomial completely.
-$10 y^{4}-19 y^{2}-15$

Accepted Answer

A)  $\left(10 y^{2}-5\right)\left(y^{2}+3\right)$ 
B)  $(5 y-3)(2 y+5)$ 
C)  $\left(2 y^{2}-5\right)\left(5 y^{2}+3\right)$ 
D)  $\left(2 y^{2}+1\right)\left(5 y^{2}-15\right)$ 
A)  $\left(10 y^{2}-5\right)\left(y^{2}+3\right)$ 
B)  $(5 y-3)(2 y+5)$ 
C)  $\left(2 y^{2}-5\right)\left(5 y^{2}+3\right)$ 
D)  $\left(2 y^{2}+1\right)\left(5 y^{2}-15\right)$

Question 7

$\mathrm{pm}+4=6 \mathrm{~m}-4 \mathrm{n}$ for $\mathrm{m}$

Accepted Answer

A)  $m=\frac{4+4 n}{p-6}$, or $m=\frac{-4-4 n}{6-p}$ 
B)  $m=\frac{-4+4 n}{p-6}$, or $m=\frac{4-4 n}{6-p}$ 
C)  $m=\frac{-4-4 n}{p-6}$, or $m=\frac{4+4 n}{6-p}$ 
D)  $m=\frac{4-4 n}{p-6}$, or $m=\frac{-4+4 n}{6-p}$ 
A)  $m=\frac{4+4 n}{p-6}$, or $m=\frac{-4-4 n}{6-p}$ 
B)  $m=\frac{-4+4 n}{p-6}$, or $m=\frac{4-4 n}{6-p}$ 
C)  $m=\frac{-4-4 n}{p-6}$, or $m=\frac{4+4 n}{6-p}$ 
D)  $m=\frac{4-4 n}{p-6}$, or $m=\frac{-4+4 n}{6-p}$

Question 8

If the polynomial $4 x^{4}+7 x^{2}-2$ is to be factored completely, is the following answer correct? Explain.
$4 x^{4}+7 x^{2}-2=\left(4 x^{2}-1\right)\left(x^{2}+2\right)$

Accepted Answer

No. The factor @#LAT-DLM& can

Question 9

Decide if the expression is factored
-$(4+7 p)(3 p-1)$

Accepted Answer

A) True 
 B)False

Question 10

Solve the equation
-$2 \mathrm{p}^{3}-9 \mathrm{p}^{2}-72 \mathrm{p}+324=0$

Accepted Answer

A)  $\{-6,6\}$ 
B)  $\left\{-6,-\frac{9}{2}, 6\right\}$ 
C)  $\{-6,0,6\}$ 
D)  $\left\{-6, \frac{9}{2}, 6\right\}$ 
A)  $\{-6,6\}$ 
B)  $\left\{-6,-\frac{9}{2}, 6\right\}$ 
C)  $\{-6,0,6\}$ 
D)  $\left\{-6, \frac{9}{2}, 6\right\}$

Question 11

Factor the trinomial completely.
-$9 z^{6}-6 z^{3}-8$

Accepted Answer

A)  $\left(3 z^{3}+1\right)\left(3 z^{3}-8\right)$ 
B)  $\left(3 z^{3}+2\right)\left(3 z^{3}-4\right)$ 
C)  $\left(3 z^{3}+4\right)\left(3 z^{3}-2\right)$ 
D)  $9\left(z^{3}-4\right)\left(z^{3}+2\right)$ 
A)  $\left(3 z^{3}+1\right)\left(3 z^{3}-8\right)$ 
B)  $\left(3 z^{3}+2\right)\left(3 z^{3}-4\right)$ 
C)  $\left(3 z^{3}+4\right)\left(3 z^{3}-2\right)$ 
D)  $9\left(z^{3}-4\right)\left(z^{3}+2\right)$

Question 12

$125 x^{6}+1$

Accepted Answer

A)  $\left(5 x^{2}-1\right)\left(25 x^{4}+5 x^{2}+1\right)$ 
B)  $\left(5 x^{2}+1\right)\left(25 x^{4}-5 x^{2}+1\right)$ 
C)  $\left(5 x^{2}+1\right)^{2}\left(5 x^{2}-1\right)$ 
D)  $\left(5 x^{2}+1\right)^{3}$ 
A)  $\left(5 x^{2}-1\right)\left(25 x^{4}+5 x^{2}+1\right)$ 
B)  $\left(5 x^{2}+1\right)\left(25 x^{4}-5 x^{2}+1\right)$ 
C)  $\left(5 x^{2}+1\right)^{2}\left(5 x^{2}-1\right)$ 
D)  $\left(5 x^{2}+1\right)^{3}$

Question 13

Find all solutions by factoring.
-$-2 b^{2}+18=0$

Accepted Answer

A)  No real solution 
B)  $\{-3,3\}$ 
C)  $\{0,3\}$ 
D)  $\{-2,3\}$ 
A)  No real solution 
B)  $\{-3,3\}$ 
C)  $\{0,3\}$ 
D)  $\{-2,3\}$

Question 14

Factor the polynomial completely
-$81 \mathrm{k}^{2}-25 \mathrm{~m}^{2}$

Accepted Answer

A)  $(81 \mathrm{k}+\mathrm{m})(\mathrm{k}-25 \mathrm{~m})$ 
B)  $(9 k-5 m)^{2}$ 
C)  $(9 k+5 m)^{2}$ 
D)  $(9 k+5 m)(9 k-5 m)$ 
A)  $(81 \mathrm{k}+\mathrm{m})(\mathrm{k}-25 \mathrm{~m})$ 
B)  $(9 k-5 m)^{2}$ 
C)  $(9 k+5 m)^{2}$ 
D)  $(9 k+5 m)(9 k-5 m)$

Question 15

The area of the rectangle shown is given by the polynomial $5 \mathrm{~W}^{2}+4 \mathrm{~W}$, where $\mathrm{W}$ represents the width. Express the length of the rectangle in terms of W.

Accepted Answer

A)  $5 W^{2}+4$ 
B)  $9 \mathrm{~W}$ 
C)  $5 W^{2}+3 W$ 
D)  $5 \mathrm{~W}+4$ 
A)  $5 W^{2}+4$ 
B)  $9 \mathrm{~W}$ 
C)  $5 W^{2}+3 W$ 
D)  $5 \mathrm{~W}+4$

Question 16

The area of the rectangle shown is $25 \mathrm{in.}^{2}$. Find the length and the width of the rectangle.

Accepted Answer

A)  length: 5 in.; width 5 in. 
B)  length: 12.5 in.; width 12.5 in. 
C)  length: 6 in.; width 4 in. 
D)  length: 13 in.; width 1 in. 
A)  length: 5 in.; width 5 in. 
B)  length: 12.5 in.; width 12.5 in. 
C)  length: 6 in.; width 4 in. 
D)  length: 13 in.; width 1 in.

Question 17

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

Accepted Answer

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

Question 18

Factor by grouping.
-$m^{2} s-m^{2} t-x s+x t$

Accepted Answer

A)  $(s-t)\left(m^{2}+x\right)$ 
B)  $\left(s-m^{2}\right)(t-x)$ 
C)  $(s-t)\left(m^{2}-x\right)$ 
D)  $(s-x)\left(m^{2}-t\right)$ 
A)  $(s-t)\left(m^{2}+x\right)$ 
B)  $\left(s-m^{2}\right)(t-x)$ 
C)  $(s-t)\left(m^{2}-x\right)$ 
D)  $(s-x)\left(m^{2}-t\right)$

Question 19

Decide if the expression is factored
-$x^{2}+20 x$

Accepted Answer

A) True 
 B)False

Question 20

$9 x+a y+a x+9 y$

Accepted Answer

A)  $(x+y)(9+a)$ 
B)  $9(x+y)+a(x+y)$ 
C)  $9 a(x+y)$ 
D)  cannot be factored 
A)  $(x+y)(9+a)$ 
B)  $9(x+y)+a(x+y)$ 
C)  $9 a(x+y)$ 
D)  cannot be factored

Factor the polynomial - $9 x^{2}-6 x+1-y^{2}$

Factor the polynomial completely - $(m-n)^{2}-8(m-n)+16$

Factor the trinomial completely. - $60 z^{6}-16 z^{4}-16 z^{2}$

Find all solutions by factoring. - $9 x^{2}=9 x$

The area of a square is given by the polynomial $25 x^{2}+30 x y+9 y^{2}$ . Find the length of a side of the square in terms of $x$ and $y$ .

Factor the trinomial completely. - $10 y^{4}-19 y^{2}-15$

$\mathrm{pm}+4=6 \mathrm{~m}-4 \mathrm{n}$ for $\mathrm{m}$

If the polynomial $4 x^{4}+7 x^{2}-2$ is to be factored completely, is the following answer correct? Explain. $4 x^{4}+7 x^{2}-2=\left(4 x^{2}-1\right)\left(x^{2}+2\right)$

Decide if the expression is factored - $(4+7 p)(3 p-1)$

Solve the equation - $2 \mathrm{p}^{3}-9 \mathrm{p}^{2}-72 \mathrm{p}+324=0$

Factor the trinomial completely. - $9 z^{6}-6 z^{3}-8$

$125 x^{6}+1$

Find all solutions by factoring. - $-2 b^{2}+18=0$

Factor the polynomial completely - $81 \mathrm{k}^{2}-25 \mathrm{~m}^{2}$

The area of the rectangle shown is $25 \mathrm{in.}^{2}$ . Find the length and the width of the rectangle. $The area of the rectangle shown is 25 \mathrm{in.}^{2} . Find the length and the width of the rectangle.$

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

Factor by grouping. - $m^{2} s-m^{2} t-x s+x t$

Decide if the expression is factored - $x^{2}+20 x$

$9 x+a y+a x+9 y$

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 - 9x2−6x+1−y29 x^{2}-6 x+1-y^{2}9x2−6x+1−y2

Factor the polynomial completely - (m−n)2−8(m−n)+16(m-n)^{2}-8(m-n)+16(m−n)2−8(m−n)+16

Factor the trinomial completely. - 60z6−16z4−16z260 z^{6}-16 z^{4}-16 z^{2}60z6−16z4−16z2

Find all solutions by factoring. - 9x2=9x9 x^{2}=9 x9x2=9x

The area of a square is given by the polynomial 25x2+30xy+9y225 x^{2}+30 x y+9 y^{2}25x2+30xy+9y2 . Find the length of a side of the square in terms of xxx and yyy .

Factor the trinomial completely. - 10y4−19y2−1510 y^{4}-19 y^{2}-1510y4−19y2−15

pm+4=6 m−4n\mathrm{pm}+4=6 \mathrm{~m}-4 \mathrm{n}pm+4=6 m−4n for m\mathrm{m}m

If the polynomial 4x4+7x2−24 x^{4}+7 x^{2}-24x4+7x2−2 is to be factored completely, is the following answer correct? Explain. 4x4+7x2−2=(4x2−1)(x2+2)4 x^{4}+7 x^{2}-2=\left(4 x^{2}-1\right)\left(x^{2}+2\right)4x4+7x2−2=(4x2−1)(x2+2)

Decide if the expression is factored - (4+7p)(3p−1)(4+7 p)(3 p-1)(4+7p)(3p−1)

Solve the equation - 2p3−9p2−72p+324=02 \mathrm{p}^{3}-9 \mathrm{p}^{2}-72 \mathrm{p}+324=02p3−9p2−72p+324=0

Factor the trinomial completely. - 9z6−6z3−89 z^{6}-6 z^{3}-89z6−6z3−8

125x6+1125 x^{6}+1125x6+1

Find all solutions by factoring. - −2b2+18=0-2 b^{2}+18=0−2b2+18=0

Factor the polynomial completely - 81k2−25 m281 \mathrm{k}^{2}-25 \mathrm{~m}^{2}81k2−25 m2

The area of the rectangle shown is given by the polynomial 5 W2+4 W5 \mathrm{~W}^{2}+4 \mathrm{~W}5 W2+4 W , where W\mathrm{W}W represents the width. Express the length of the rectangle in terms of W.

The area of the rectangle shown is 25in.225 \mathrm{in.}^{2}25in.2 . Find the length and the width of the rectangle.

Factor the polynomial completely - n4+n3+n+1n^{4}+n^{3}+n+1n4+n3+n+1

Factor by grouping. - m2s−m2t−xs+xtm^{2} s-m^{2} t-x s+x tm2s−m2t−xs+xt

Decide if the expression is factored - x2+20xx^{2}+20 xx2+20x

9x+ay+ax+9y9 x+a y+a x+9 y9x+ay+ax+9y

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 - $9 x^{2}-6 x+1-y^{2}$

Factor the polynomial completely - $(m-n)^{2}-8(m-n)+16$

Factor the trinomial completely. - $60 z^{6}-16 z^{4}-16 z^{2}$

Find all solutions by factoring. - $9 x^{2}=9 x$

The area of a square is given by the polynomial $25 x^{2}+30 x y+9 y^{2}$ . Find the length of a side of the square in terms of $x$ and $y$ .

Factor the trinomial completely. - $10 y^{4}-19 y^{2}-15$

$\mathrm{pm}+4=6 \mathrm{~m}-4 \mathrm{n}$ for $\mathrm{m}$

If the polynomial $4 x^{4}+7 x^{2}-2$ is to be factored completely, is the following answer correct? Explain. $4 x^{4}+7 x^{2}-2=\left(4 x^{2}-1\right)\left(x^{2}+2\right)$

Decide if the expression is factored - $(4+7 p)(3 p-1)$

Solve the equation - $2 \mathrm{p}^{3}-9 \mathrm{p}^{2}-72 \mathrm{p}+324=0$

Factor the trinomial completely. - $9 z^{6}-6 z^{3}-8$

$125 x^{6}+1$

Find all solutions by factoring. - $-2 b^{2}+18=0$

Factor the polynomial completely - $81 \mathrm{k}^{2}-25 \mathrm{~m}^{2}$

The area of the rectangle shown is $25 \mathrm{in.}^{2}$ . Find the length and the width of the rectangle. $The area of the rectangle shown is 25 \mathrm{in.}^{2} . Find the length and the width of the rectangle.$

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

Factor by grouping. - $m^{2} s-m^{2} t-x s+x t$

Decide if the expression is factored - $x^{2}+20 x$

$9 x+a y+a x+9 y$