Question 1

Factor the polynomial completely
-$25 k^{2}-64 m^{2}$

Accepted Answer

A)  $(5 k+8 m)(5 k-8 m)$ 
B)  $(5 k-8 m)^{2}$ 
C)  $(25 k+m)(k-64 m)$ 
D)  $(5 k+8 m)^{2}$ 
A)  $(5 k+8 m)(5 k-8 m)$ 
B)  $(5 k-8 m)^{2}$ 
C)  $(25 k+m)(k-64 m)$ 
D)  $(5 k+8 m)^{2}$

Question 2

Factor the polynomial completely
-$25 y^{4}-16$

Accepted Answer

A)  $\left(5 y^{2}-4\right)^{2}$ 
B)  $\left(5 y^{2}+4\right)\left(5 y^{2}-4\right)$ 
C)  $\left(5 y^{2}+4\right)^{2}$ 
D)  $\left(25 y^{2}+1\right)\left(y^{2}-16\right)$ 
A)  $\left(5 y^{2}-4\right)^{2}$ 
B)  $\left(5 y^{2}+4\right)\left(5 y^{2}-4\right)$ 
C)  $\left(5 y^{2}+4\right)^{2}$ 
D)  $\left(25 y^{2}+1\right)\left(y^{2}-16\right)$

Question 3

Find all solutions by factoring.
-$(5 x+6)(x+3)=-23 x-45$

Accepted Answer

A)  $\left\{-\frac{45}{28},-3\right\}$ 
B)  $\left\{-\frac{9}{5},-7\right\}$ 
C)  $\left\{-\frac{15}{8},-\frac{45}{28}\right\}$ 
D)  $\left\{-\frac{6}{5},-\frac{45}{23},-3\right\}$ 
A)  $\left\{-\frac{45}{28},-3\right\}$ 
B)  $\left\{-\frac{9}{5},-7\right\}$ 
C)  $\left\{-\frac{15}{8},-\frac{45}{28}\right\}$ 
D)  $\left\{-\frac{6}{5},-\frac{45}{23},-3\right\}$

Question 4

Factor by grouping.
-$14 r^{2}+63 r y-2 x r-9 x y$

Accepted Answer

A)  $(2 r+9 y)(7 r-x)$ 
B)  $(9 r+2 y)(7 r-x)$ 
C)  $(2 r+9 y)(x-7 r)$ 
D)  $(2 r+9 y)(7 x-r)$ 
A)  $(2 r+9 y)(7 r-x)$ 
B)  $(9 r+2 y)(7 r-x)$ 
C)  $(2 r+9 y)(x-7 r)$ 
D)  $(2 r+9 y)(7 x-r)$

Question 5

Without actually solving each equation, determine which one of the following has 0 in its solution set. Explain your answer.
$$\begin{aligned}
& r^{3}+5 r^{2}=-9 r \
& 4 m^{2}-64=0 \
& n^{2}-9 n+9=0 \
& -3 s-8 s+5=0
\end{aligned}$$

Accepted Answer

@#LAT-DLM& This has 0 in its s

Question 6

actor out the greatest common factor. Simplify the factors, if possible
-$(x-6)(x+7)+(x-6)(x+3)$

Accepted Answer

A)  $(x-6)(2 x+10)$ 
B)  $2(x-6)(x+5)$ 
C)  $2(x-6)(2 x+10)$ 
D)  $(x-6)(x+10)$ 
A)  $(x-6)(2 x+10)$ 
B)  $2(x-6)(x+5)$ 
C)  $2(x-6)(2 x+10)$ 
D)  $(x-6)(x+10)$

Question 7

Factor the polynomial completely
-$w^{2}+10 w+25-z^{2}$

Accepted Answer

A)  $(w+5+z)(w+5-z)$ 
B)  $(w-5+z)(w+5-z)$ 
C)  $(w-5+z)(w-5-z)$ 
D)  $(-w+25+z)(w+25-z)$ 
A)  $(w+5+z)(w+5-z)$ 
B)  $(w-5+z)(w+5-z)$ 
C)  $(w-5+z)(w-5-z)$ 
D)  $(-w+25+z)(w+25-z)$

Question 8

$25 a^{2}+60 a b+36 b^{2}$

Accepted Answer

A)  $(5 a+6 b)(5 a-6 b)$ 
B)  $30(a+b)(a-b)$ 
C)  $2(5 a+6 b)$ 
D)  $(5 a+6 b)^{2}$ 
A)  $(5 a+6 b)(5 a-6 b)$ 
B)  $30(a+b)(a-b)$ 
C)  $2(5 a+6 b)$ 
D)  $(5 a+6 b)^{2}$

Question 9

Factor the trinomial completely.
-$-2 x^{2}-2 x+84$

Accepted Answer

A)  $-2(x+6)(x-7)$ 
B)  $2(x-6)(x+7)$ 
C)  $-2(x-6)(x+7)$ 
D)  $-2(x+6)(x+7)$ 
A)  $-2(x+6)(x-7)$ 
B)  $2(x-6)(x+7)$ 
C)  $-2(x-6)(x+7)$ 
D)  $-2(x+6)(x+7)$

Question 10

What value of $n$ will make $x^{n}$ a perfect cube?

Accepted Answer

A)  It is not possible for any $n$. 
B)  $n$ must be a multiple of 5 . 
C)  $n$ must be a multiple of 2 . 
D)  $n$ must be a multiple of 3 . 
A)  It is not possible for any $n$. 
B)  $n$ must be a multiple of 5 . 
C)  $n$ must be a multiple of 2 . 
D)  $n$ must be a multiple of 3 .

Question 11

actor out the greatest common factor. Simplify the factors, if possible
-$5 \mathrm{~m}(2-\mathrm{m})+6 n(2-\mathrm{m})$

Accepted Answer

A)  $(5 m-6 n)(2-m)$ 
B)  $m(5+6 n)(2-m)$ 
C)  $5(m+n)(2-m)$ 
D)  $(5 m+6 n)(2-m)$ 
A)  $(5 m-6 n)(2-m)$ 
B)  $m(5+6 n)(2-m)$ 
C)  $5(m+n)(2-m)$ 
D)  $(5 m+6 n)(2-m)$

Question 12

Factor the trinomial completely.
-$8 z^{4}-6 z^{2}-9$

Accepted Answer

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

Question 13

Factor the polynomial completely
-$12 x^{2}+25 x+12$

Accepted Answer

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

Question 14

Factor out the variable that is raised to the smaller exponent
-$x^{-6}-7 x^{-9}$

Accepted Answer

A)  $x^{-9}\left(7 x^{3}\right)$ 
B)  $x^{-9}\left(x^{3}-7\right)$ 
C)  $x^{-9}\left(x^{3}+7\right)$ 
D)  $x^{-9}\left(x^{-3}-7\right)$ 
A)  $x^{-9}\left(7 x^{3}\right)$ 
B)  $x^{-9}\left(x^{3}-7\right)$ 
C)  $x^{-9}\left(x^{3}+7\right)$ 
D)  $x^{-9}\left(x^{-3}-7\right)$

Question 15

Factor by grouping.
-$s m+t m+s b+t b$

Accepted Answer

A)  $(s+b)(m+t)$ 
B)  $(s+t)(m+b)$ 
C)  $(\mathrm{s}+\mathrm{t})(\mathrm{m}+\mathrm{t})$ 
D)  $(\mathrm{s}+\mathrm{m})(\mathrm{t}+\mathrm{b})$ 
A)  $(s+b)(m+t)$ 
B)  $(s+t)(m+b)$ 
C)  $(\mathrm{s}+\mathrm{t})(\mathrm{m}+\mathrm{t})$ 
D)  $(\mathrm{s}+\mathrm{m})(\mathrm{t}+\mathrm{b})$

Question 16

Factor the polynomial completely
-$x^{2}-x-6$

Accepted Answer

A)  $(x-3)(x+3)$ 
B)  $(x+2)(x-3)$ 
C)  $(x+1)(x-5)$ 
D)  $(x+3)(x-2)$ 
A)  $(x-3)(x+3)$ 
B)  $(x+2)(x-3)$ 
C)  $(x+1)(x-5)$ 
D)  $(x+3)(x-2)$

Question 17

A room has an area of 208 square feet. One dimension is 3 feet more than the other. Find the dimensions of the room.

Accepted Answer

A)  16 feet, 19 feet 
B)  10 feet, 13 feet 
C)  14 feet, 17 feet 
D)  13 feet, 16 feet 
A)  16 feet, 19 feet 
B)  10 feet, 13 feet 
C)  14 feet, 17 feet 
D)  13 feet, 16 feet

Question 18

Factor the trinomial completely.
-$\mathrm{u}^{2}-2 \mathrm{uv}-15 \mathrm{v}^{2}$

Accepted Answer

A)  $(u-v)(u+5 v)$ 
B)  $(u-3 v)(u+5 v)$ 
C)  $(u-3 v)(u+v)$ 
D)  $(u+3 v)(u-5 v)$ 
A)  $(u-v)(u+5 v)$ 
B)  $(u-3 v)(u+5 v)$ 
C)  $(u-3 v)(u+v)$ 
D)  $(u+3 v)(u-5 v)$

Question 19

Factor the trinomial completely.
-$-2 x^{3}-10 x^{2}+28 x$

Accepted Answer

A)  $2 x(x+2)(x+7)$ 
B)  $-2 x(x+2)(x-7)$ 
C)  $-2 x(x-2)(x+7)$ 
D)  $-2 x^{2}(x-2)(x-7)$ 
A)  $2 x(x+2)(x+7)$ 
B)  $-2 x(x+2)(x-7)$ 
C)  $-2 x(x-2)(x+7)$ 
D)  $-2 x^{2}(x-2)(x-7)$

Question 20

Solve the equation.
-$(x-6)(x+4)=0$

Accepted Answer

A)  $\{-6,4\}$ 
B)  $\{6,4\}$ 
C)  $\{ \pm 6, \pm 4\}$ 
D)  $\{6,-4\}$ 
A)  $\{-6,4\}$ 
B)  $\{6,4\}$ 
C)  $\{ \pm 6, \pm 4\}$ 
D)  $\{6,-4\}$

Factor the polynomial completely - $25 k^{2}-64 m^{2}$

Factor the polynomial completely - $25 y^{4}-16$

Find all solutions by factoring. - $(5 x+6)(x+3)=-23 x-45$

Factor by grouping. - $14 r^{2}+63 r y-2 x r-9 x y$

Without actually solving each equation, determine which one of the following has 0 in its solution set. Explain your answer. +5=-9r 4-64=0 -9n+9=0 -3s-8s+5=0

actor out the greatest common factor. Simplify the factors, if possible - $(x-6)(x+7)+(x-6)(x+3)$

Factor the polynomial completely - $w^{2}+10 w+25-z^{2}$

$25 a^{2}+60 a b+36 b^{2}$

Factor the trinomial completely. - $-2 x^{2}-2 x+84$

What value of $n$ will make $x^{n}$ a perfect cube?

actor out the greatest common factor. Simplify the factors, if possible - $5 \mathrm{~m}(2-\mathrm{m})+6 n(2-\mathrm{m})$

Factor the trinomial completely. - $8 z^{4}-6 z^{2}-9$

Factor the polynomial completely - $12 x^{2}+25 x+12$

Factor out the variable that is raised to the smaller exponent - $x^{-6}-7 x^{-9}$

Factor by grouping. - $s m+t m+s b+t b$

Factor the polynomial completely - $x^{2}-x-6$

A room has an area of 208 square feet. One dimension is 3 feet more than the other. Find the dimensions of the room.

Factor the trinomial completely. - $\mathrm{u}^{2}-2 \mathrm{uv}-15 \mathrm{v}^{2}$

Factor the trinomial completely. - $-2 x^{3}-10 x^{2}+28 x$

Solve the equation. - $(x-6)(x+4)=0$

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 - 25k2−64m225 k^{2}-64 m^{2}25k2−64m2

Factor the polynomial completely - 25y4−1625 y^{4}-1625y4−16

Find all solutions by factoring. - (5x+6)(x+3)=−23x−45(5 x+6)(x+3)=-23 x-45(5x+6)(x+3)=−23x−45

Factor by grouping. - 14r2+63ry−2xr−9xy14 r^{2}+63 r y-2 x r-9 x y14r2+63ry−2xr−9xy

Without actually solving each equation, determine which one of the following has 0 in its solution set. Explain your answer. +5=-9r 4-64=0 -9n+9=0 -3s-8s+5=0

actor out the greatest common factor. Simplify the factors, if possible - (x−6)(x+7)+(x−6)(x+3)(x-6)(x+7)+(x-6)(x+3)(x−6)(x+7)+(x−6)(x+3)

Factor the polynomial completely - w2+10w+25−z2w^{2}+10 w+25-z^{2}w2+10w+25−z2

25a2+60ab+36b225 a^{2}+60 a b+36 b^{2}25a2+60ab+36b2

Factor the trinomial completely. - −2x2−2x+84-2 x^{2}-2 x+84−2x2−2x+84

What value of nnn will make xnx^{n}xn a perfect cube?

actor out the greatest common factor. Simplify the factors, if possible - 5 m(2−m)+6n(2−m)5 \mathrm{~m}(2-\mathrm{m})+6 n(2-\mathrm{m})5 m(2−m)+6n(2−m)

Factor the trinomial completely. - 8z4−6z2−98 z^{4}-6 z^{2}-98z4−6z2−9

Factor the polynomial completely - 12x2+25x+1212 x^{2}+25 x+1212x2+25x+12

Factor out the variable that is raised to the smaller exponent - x−6−7x−9x^{-6}-7 x^{-9}x−6−7x−9

Factor by grouping. - sm+tm+sb+tbs m+t m+s b+t bsm+tm+sb+tb

Factor the polynomial completely - x2−x−6x^{2}-x-6x2−x−6

A room has an area of 208 square feet. One dimension is 3 feet more than the other. Find the dimensions of the room.

Factor the trinomial completely. - u2−2uv−15v2\mathrm{u}^{2}-2 \mathrm{uv}-15 \mathrm{v}^{2}u2−2uv−15v2

Factor the trinomial completely. - −2x3−10x2+28x-2 x^{3}-10 x^{2}+28 x−2x3−10x2+28x

Solve the equation. - (x−6)(x+4)=0(x-6)(x+4)=0(x−6)(x+4)=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 - $25 k^{2}-64 m^{2}$

Factor the polynomial completely - $25 y^{4}-16$

Find all solutions by factoring. - $(5 x+6)(x+3)=-23 x-45$

Factor by grouping. - $14 r^{2}+63 r y-2 x r-9 x y$

actor out the greatest common factor. Simplify the factors, if possible - $(x-6)(x+7)+(x-6)(x+3)$

Factor the polynomial completely - $w^{2}+10 w+25-z^{2}$

$25 a^{2}+60 a b+36 b^{2}$

Factor the trinomial completely. - $-2 x^{2}-2 x+84$

What value of $n$ will make $x^{n}$ a perfect cube?

actor out the greatest common factor. Simplify the factors, if possible - $5 \mathrm{~m}(2-\mathrm{m})+6 n(2-\mathrm{m})$

Factor the trinomial completely. - $8 z^{4}-6 z^{2}-9$

Factor the polynomial completely - $12 x^{2}+25 x+12$

Factor out the variable that is raised to the smaller exponent - $x^{-6}-7 x^{-9}$

Factor by grouping. - $s m+t m+s b+t b$

Factor the polynomial completely - $x^{2}-x-6$

Factor the trinomial completely. - $\mathrm{u}^{2}-2 \mathrm{uv}-15 \mathrm{v}^{2}$

Factor the trinomial completely. - $-2 x^{3}-10 x^{2}+28 x$

Solve the equation. - $(x-6)(x+4)=0$