Question 1

Factor the polynomial completely
-$25 s^{2}-16 t^{4}$

Accepted Answer

A)  $\left(5 \mathrm{~s}+4 \mathrm{t}^{2}\right)^{2}$ 
B)  $\left(25 \mathrm{~s}+\mathrm{t}^{2}\right)\left(\mathrm{s}-16 \mathrm{t}^{2}\right)$ 
C)  $\left(5 \mathrm{~s}-4 \mathrm{t}^{2}\right)^{2}$ 
D)  $\left(5 \mathrm{~s}+4 \mathrm{t}^{2}\right)\left(5 \mathrm{~s}-4 \mathrm{t}^{2}\right)$ 
A)  $\left(5 \mathrm{~s}+4 \mathrm{t}^{2}\right)^{2}$ 
B)  $\left(25 \mathrm{~s}+\mathrm{t}^{2}\right)\left(\mathrm{s}-16 \mathrm{t}^{2}\right)$ 
C)  $\left(5 \mathrm{~s}-4 \mathrm{t}^{2}\right)^{2}$ 
D)  $\left(5 \mathrm{~s}+4 \mathrm{t}^{2}\right)\left(5 \mathrm{~s}-4 \mathrm{t}^{2}\right)$

Question 2

Factor the polynomial completely
-$9 y^{2}+18 y+8$

Accepted Answer

A)  $(9 y+2)(y+4)$ 
B)  $(3 y+2)(3 y+4)$ 
C)  $(9 y+1)(y-8)$ 
D)  $(3 y-2)(3 y-4)$ 
A)  $(9 y+2)(y+4)$ 
B)  $(3 y+2)(3 y+4)$ 
C)  $(9 y+1)(y-8)$ 
D)  $(3 y-2)(3 y-4)$

Question 3

Factor the trinomial completely.
-$4 x^{3}+4 x^{2}-48 x$

Accepted Answer

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

Question 4

actor out the greatest common factor. Simplify the factors, if possible
-$40 x^{8} y^{8}-48 x^{3} y^{6}-56 x^{6} y^{2}$

Accepted Answer

A)  $x^{3} y^{2}\left(40 x^{5} y^{6}-48 y^{4}-56 x^{3}\right)$ 
B)  $8\left(5 x^{8} y^{8}-6 x^{3} y^{6}-7 x^{6} y^{2}\right)$ 
C)  $8 x^{3} y^{2}\left(5 x^{5} y^{6}-6 y^{4}-7 x^{3}\right)$ 
D)  $8 x^{3}\left(5 x^{5} y^{8}-6 y^{6}-7 x^{3} y^{2}\right)$ 
A)  $x^{3} y^{2}\left(40 x^{5} y^{6}-48 y^{4}-56 x^{3}\right)$ 
B)  $8\left(5 x^{8} y^{8}-6 x^{3} y^{6}-7 x^{6} y^{2}\right)$ 
C)  $8 x^{3} y^{2}\left(5 x^{5} y^{6}-6 y^{4}-7 x^{3}\right)$ 
D)  $8 x^{3}\left(5 x^{5} y^{8}-6 y^{6}-7 x^{3} y^{2}\right)$

Question 5

A student says that the equation
$(a+8)(a-1)=12$ can be solved as follows: $a+8=2$ or $a-1=6$.
If this is correct, explain why. If it is not correct, explain why and give the correct method.

Accepted Answer

This is not correct. The zero-factor pro

Question 6

Why is the answer $\left(x^{2}-196\right)\left(x^{2}+196\right)$ not the correct solution to the instruction to factor the polynomial $x^{4}-38,416$ completely?

Accepted Answer

The polynomial has not been fa

Question 7

Find all solutions by factoring.
-$2 x^{2}+30=x^{2}+11 x$

Accepted Answer

A)  $\{6,5\}$ 
B)  $\{15\}$ 
C)  $\left\{\frac{11}{2},-6\right\}$ 
D)  $\left\{15, \frac{11}{2}\right\}$ 
A)  $\{6,5\}$ 
B)  $\{15\}$ 
C)  $\left\{\frac{11}{2},-6\right\}$ 
D)  $\left\{15, \frac{11}{2}\right\}$

Question 8

Find all solutions by factoring.
-$-\mathrm{x}^{2}=16-8 \mathrm{x}$

Accepted Answer

A)  $\{0,\}$ 
B)  $\{-4\}$ 
C)  $\{4\}$ 
D)  $\{-4,4\}$ 
A)  $\{0,\}$ 
B)  $\{-4\}$ 
C)  $\{4\}$ 
D)  $\{-4,4\}$

Question 9

actor out the greatest common factor. Simplify the factors, if possible
-$2(m+p)^{3}-12(m+p)^{2}-6(m+p)^{4}$

Accepted Answer

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

Question 10

Factor the polynomial completely
-$49 s^{2}-81 t^{4}$

Accepted Answer

A)  $\left(7 s-9 t^{2}\right)^{2}$ 
B)  $\left(7 s+9 t^{2}\right)^{2}$ 
C)  $\left(49 \mathrm{~s}+\mathrm{t}^{2}\right)\left(\mathrm{s}-81 \mathrm{t}^{2}\right)$ 
D)  $\left(7 \mathrm{~s}+9 \mathrm{t}^{2}\right)\left(7 \mathrm{~s}-9 \mathrm{t}^{2}\right)$ 
A)  $\left(7 s-9 t^{2}\right)^{2}$ 
B)  $\left(7 s+9 t^{2}\right)^{2}$ 
C)  $\left(49 \mathrm{~s}+\mathrm{t}^{2}\right)\left(\mathrm{s}-81 \mathrm{t}^{2}\right)$ 
D)  $\left(7 \mathrm{~s}+9 \mathrm{t}^{2}\right)\left(7 \mathrm{~s}-9 \mathrm{t}^{2}\right)$

Question 11

actor out the greatest common factor. Simplify the factors, if possible
-$2 x(3 x-4)-3(3 x-4)$

Accepted Answer

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

Question 12

A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?

Accepted Answer

A)  10 feet 
B)  4 feet 
C)  5 feet 
D)  3 feet 
A)  10 feet 
B)  4 feet 
C)  5 feet 
D)  3 feet

Question 13

Factor the polynomial completely
-$3 x^{3}+3 x^{2} y-60 x y^{2}$

Accepted Answer

A)  $(x-4 y)\left(3 x^{2}+15 x y\right)$ 
B)  $3 x(x+4 y)(x-5 y)$ 
C)  $\left(3 x^{2}+12 x y\right)(x-5 y)$ 
D)  $3 x(x-4 y)(x+5 y)$ 
A)  $(x-4 y)\left(3 x^{2}+15 x y\right)$ 
B)  $3 x(x+4 y)(x-5 y)$ 
C)  $\left(3 x^{2}+12 x y\right)(x-5 y)$ 
D)  $3 x(x-4 y)(x+5 y)$

Question 14

Factor by grouping.
-$x^{3}+7 x^{2}-10 x-70$

Accepted Answer

A)  $\left(x^{2}+7\right)(x-10)$ 
B)  $(x+7)\left(x^{2}-10\right)$ 
C)  $(x+7)\left(x^{3}-10 x\right)$ 
D)  $(x-7)\left(x^{2}-10\right)$ 
A)  $\left(x^{2}+7\right)(x-10)$ 
B)  $(x+7)\left(x^{2}-10\right)$ 
C)  $(x+7)\left(x^{3}-10 x\right)$ 
D)  $(x-7)\left(x^{2}-10\right)$

Question 15

Is the following solution to the equation $81 x^{3}=4 x$ correct? Explain.
$$\begin{aligned}
& 81 x^{3}=4 x \
& 81 x^{2}=4 \
& 9 x=2 \text { or }-2 \
& x=\frac{2}{9} \text { or } x=-\frac{2}{9} \
& \left\{-\frac{2}{9}, \frac{2}{9}\right\}
\end{aligned}$$

Accepted Answer

This solution is not correct. In the div

Question 16

Factor the trinomial completely.
-$40 m^{2} n^{2}-41 m n+10$

Accepted Answer

A)  $\left(8 m^{2}-5\right)\left(5 n^{2}-2\right)$ 
B)  $(8 m n+5)(5 m n+2)$ 
C)  $(8 \mathrm{mn}-5)(5 \mathrm{mn}+2)$ 
D)  $(8 m n-5)(5 m n-2)$ 
A)  $\left(8 m^{2}-5\right)\left(5 n^{2}-2\right)$ 
B)  $(8 m n+5)(5 m n+2)$ 
C)  $(8 \mathrm{mn}-5)(5 \mathrm{mn}+2)$ 
D)  $(8 m n-5)(5 m n-2)$

Question 17

Solve the equation
-$(3 \mathrm{x}-1)^{2}=25 \mathrm{x}^{2}$

Accepted Answer

A)  $\left\{-\frac{1}{2}, \frac{1}{8}\right\}$ 
B)  $\left\{-\frac{2}{5},-\frac{5}{2}\right\}$ 
C)  $\left\{\frac{1}{3},-\frac{1}{3}\right\}$ 
D)  $\left\{-\frac{1}{2}\right\}$ 
A)  $\left\{-\frac{1}{2}, \frac{1}{8}\right\}$ 
B)  $\left\{-\frac{2}{5},-\frac{5}{2}\right\}$ 
C)  $\left\{\frac{1}{3},-\frac{1}{3}\right\}$ 
D)  $\left\{-\frac{1}{2}\right\}$

Question 18

If an object is projected upward with an initial velocity of $96 \mathrm{ft}$ per sec from a height $\mathrm{h}$ of $256 \mathrm{ft}$, then its height $t$ sec after it is projected is defined by the equation $h=-16 t^{2}+96 t+256$. How many sec after it is projected will it hit the ground?

Accepted Answer

A)  $10 \mathrm{sec}$ 
B)  $8 \mathrm{sec}$ 
C)  $2 \mathrm{sec}$ 
D)  $9 \mathrm{sec}$ 
A)  $10 \mathrm{sec}$ 
B)  $8 \mathrm{sec}$ 
C)  $2 \mathrm{sec}$ 
D)  $9 \mathrm{sec}$

Question 19

Decide if the expression is factored
-$3(m-2)+n(m-2)$

Accepted Answer

A) True 
 B)False

Question 20

Factor the polynomial completely
-$10 a^{3}+25 a^{2} b+4 a b^{2}+10 b^{3}$

Accepted Answer

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

Factor the polynomial completely - $25 s^{2}-16 t^{4}$

Factor the polynomial completely - $9 y^{2}+18 y+8$

Factor the trinomial completely. - $4 x^{3}+4 x^{2}-48 x$

actor out the greatest common factor. Simplify the factors, if possible - $40 x^{8} y^{8}-48 x^{3} y^{6}-56 x^{6} y^{2}$

A student says that the equation $(a+8)(a-1)=12$ can be solved as follows: $a+8=2$ or $a-1=6$ . If this is correct, explain why. If it is not correct, explain why and give the correct method.

Why is the answer $\left(x^{2}-196\right)\left(x^{2}+196\right)$ not the correct solution to the instruction to factor the polynomial $x^{4}-38,416$ completely?

Find all solutions by factoring. - $2 x^{2}+30=x^{2}+11 x$

Find all solutions by factoring. - $-\mathrm{x}^{2}=16-8 \mathrm{x}$

actor out the greatest common factor. Simplify the factors, if possible - $2(m+p)^{3}-12(m+p)^{2}-6(m+p)^{4}$

Factor the polynomial completely - $49 s^{2}-81 t^{4}$

actor out the greatest common factor. Simplify the factors, if possible - $2 x(3 x-4)-3(3 x-4)$

A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?

Factor the polynomial completely - $3 x^{3}+3 x^{2} y-60 x y^{2}$

Factor by grouping. - $x^{3}+7 x^{2}-10 x-70$

Is the following solution to the equation $81 x^{3}=4 x$ correct? Explain. 81=4x 81=4 9x=2 or -2 x= or x=- -,

Factor the trinomial completely. - $40 m^{2} n^{2}-41 m n+10$

Solve the equation - $(3 \mathrm{x}-1)^{2}=25 \mathrm{x}^{2}$

If an object is projected upward with an initial velocity of $96 \mathrm{ft}$ per sec from a height $\mathrm{h}$ of $256 \mathrm{ft}$ , then its height $t$ sec after it is projected is defined by the equation $h=-16 t^{2}+96 t+256$ . How many sec after it is projected will it hit the ground?

Decide if the expression is factored - $3(m-2)+n(m-2)$

Factor the polynomial completely - $10 a^{3}+25 a^{2} b+4 a b^{2}+10 b^{3}$

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 - 25s2−16t425 s^{2}-16 t^{4}25s2−16t4

Factor the polynomial completely - 9y2+18y+89 y^{2}+18 y+89y2+18y+8

Factor the trinomial completely. - 4x3+4x2−48x4 x^{3}+4 x^{2}-48 x4x3+4x2−48x

actor out the greatest common factor. Simplify the factors, if possible - 40x8y8−48x3y6−56x6y240 x^{8} y^{8}-48 x^{3} y^{6}-56 x^{6} y^{2}40x8y8−48x3y6−56x6y2

A student says that the equation (a+8)(a−1)=12(a+8)(a-1)=12(a+8)(a−1)=12 can be solved as follows: a+8=2a+8=2a+8=2 or a−1=6a-1=6a−1=6 . If this is correct, explain why. If it is not correct, explain why and give the correct method.

Why is the answer (x2−196)(x2+196)\left(x^{2}-196\right)\left(x^{2}+196\right)(x2−196)(x2+196) not the correct solution to the instruction to factor the polynomial x4−38,416x^{4}-38,416x4−38,416 completely?

Find all solutions by factoring. - 2x2+30=x2+11x2 x^{2}+30=x^{2}+11 x2x2+30=x2+11x

Find all solutions by factoring. - −x2=16−8x-\mathrm{x}^{2}=16-8 \mathrm{x}−x2=16−8x

actor out the greatest common factor. Simplify the factors, if possible - 2(m+p)3−12(m+p)2−6(m+p)42(m+p)^{3}-12(m+p)^{2}-6(m+p)^{4}2(m+p)3−12(m+p)2−6(m+p)4

Factor the polynomial completely - 49s2−81t449 s^{2}-81 t^{4}49s2−81t4

actor out the greatest common factor. Simplify the factors, if possible - 2x(3x−4)−3(3x−4)2 x(3 x-4)-3(3 x-4)2x(3x−4)−3(3x−4)

A rectangular garden is 12 feet by 5 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 138 square feet?

Factor the polynomial completely - 3x3+3x2y−60xy23 x^{3}+3 x^{2} y-60 x y^{2}3x3+3x2y−60xy2

Factor by grouping. - x3+7x2−10x−70x^{3}+7 x^{2}-10 x-70x3+7x2−10x−70

Is the following solution to the equation 81x3=4x81 x^{3}=4 x81x3=4x correct? Explain. 81=4x 81=4 9x=2 or -2 x= or x=- -,

Factor the trinomial completely. - 40m2n2−41mn+1040 m^{2} n^{2}-41 m n+1040m2n2−41mn+10

Solve the equation - (3x−1)2=25x2(3 \mathrm{x}-1)^{2}=25 \mathrm{x}^{2}(3x−1)2=25x2

Decide if the expression is factored - 3(m−2)+n(m−2)3(m-2)+n(m-2)3(m−2)+n(m−2)

Factor the polynomial completely - 10a3+25a2b+4ab2+10b310 a^{3}+25 a^{2} b+4 a b^{2}+10 b^{3}10a3+25a2b+4ab2+10b3

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 - $25 s^{2}-16 t^{4}$

Factor the polynomial completely - $9 y^{2}+18 y+8$

Factor the trinomial completely. - $4 x^{3}+4 x^{2}-48 x$

actor out the greatest common factor. Simplify the factors, if possible - $40 x^{8} y^{8}-48 x^{3} y^{6}-56 x^{6} y^{2}$

A student says that the equation $(a+8)(a-1)=12$ can be solved as follows: $a+8=2$ or $a-1=6$ . If this is correct, explain why. If it is not correct, explain why and give the correct method.

Why is the answer $\left(x^{2}-196\right)\left(x^{2}+196\right)$ not the correct solution to the instruction to factor the polynomial $x^{4}-38,416$ completely?

Find all solutions by factoring. - $2 x^{2}+30=x^{2}+11 x$

Find all solutions by factoring. - $-\mathrm{x}^{2}=16-8 \mathrm{x}$

actor out the greatest common factor. Simplify the factors, if possible - $2(m+p)^{3}-12(m+p)^{2}-6(m+p)^{4}$

Factor the polynomial completely - $49 s^{2}-81 t^{4}$

actor out the greatest common factor. Simplify the factors, if possible - $2 x(3 x-4)-3(3 x-4)$

Factor the polynomial completely - $3 x^{3}+3 x^{2} y-60 x y^{2}$

Factor by grouping. - $x^{3}+7 x^{2}-10 x-70$

Is the following solution to the equation $81 x^{3}=4 x$ correct? Explain. 81=4x 81=4 9x=2 or -2 x= or x=- -,

Factor the trinomial completely. - $40 m^{2} n^{2}-41 m n+10$

Solve the equation - $(3 \mathrm{x}-1)^{2}=25 \mathrm{x}^{2}$

Decide if the expression is factored - $3(m-2)+n(m-2)$

Factor the polynomial completely - $10 a^{3}+25 a^{2} b+4 a b^{2}+10 b^{3}$