Question 1

$6 x^{2}-7 x-24$

Accepted Answer

A)  $(2 x-3)(3 x+8)$ 
B)  $(6 x-8)(x+3)$ 
C)  $(6 x-7)(x+24)$ 
D)  $(2 x+3)(3 x-8)$ 
A)  $(2 x-3)(3 x+8)$ 
B)  $(6 x-8)(x+3)$ 
C)  $(6 x-7)(x+24)$ 
D)  $(2 x+3)(3 x-8)$

Question 2

A farmer has 260 meters of fencing and wants to enclose a rectangular area of 3600 square meters. What dimensions should he use?

Accepted Answer

A)  65 meters by 65 meters 
B)  $\sqrt{3600}$ meters by $\sqrt{3600}$ meters 
C)  90 meters by 40 meters 
D)  180 meters by 2 meters 
A)  65 meters by 65 meters 
B)  $\sqrt{3600}$ meters by $\sqrt{3600}$ meters 
C)  90 meters by 40 meters 
D)  180 meters by 2 meters

Question 3

Factor by grouping.
-11) $7 y+7 a-y^{2}-y a$

Accepted Answer

A)  $(y-a)(7-y)$ 
B)  $(y+a)(7-y)$ 
C)  $(y+a)(7-a)$ 
D)  $(y-a)(7+y)$ 
A)  $(y-a)(7-y)$ 
B)  $(y+a)(7-y)$ 
C)  $(y+a)(7-a)$ 
D)  $(y-a)(7+y)$

Question 4

Factor the polynomial completely
-$1-1296 \mathrm{~m}^{4}$

Accepted Answer

A)  $\left(1+36 \mathrm{~m}^{2}\right)\left(1-36 \mathrm{~m}^{2}\right)$ 
B)  $(1+6 m)^{2}(1-6 m)^{2}$ 
C)  $1-1296 \mathrm{~m}^{4}$ 
D)  $(1+6 m)(1-6 m)\left(1+36 m^{2}\right)$ 
A)  $\left(1+36 \mathrm{~m}^{2}\right)\left(1-36 \mathrm{~m}^{2}\right)$ 
B)  $(1+6 m)^{2}(1-6 m)^{2}$ 
C)  $1-1296 \mathrm{~m}^{4}$ 
D)  $(1+6 m)(1-6 m)\left(1+36 m^{2}\right)$

Question 5

Factor the polynomial completely
-$40 x^{3}+14 x^{2}-12 x$

Accepted Answer

A)  $2\left(4 x^{2}+3\right)(5 x-2)$ 
B)  $2 x(4 x+3)(5 x-2)$ 
C)  $x(2 x+6)(5 x-2)$ 
D)  $x(4 x+3)(10 x-4)$ 
A)  $2\left(4 x^{2}+3\right)(5 x-2)$ 
B)  $2 x(4 x+3)(5 x-2)$ 
C)  $x(2 x+6)(5 x-2)$ 
D)  $x(4 x+3)(10 x-4)$

Question 6

Factor by grouping.
-$x^{3}+4 x^{2}+2 x+8$

Accepted Answer

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

Question 7

Factor the polynomial
-$r^{2}+2 r s+s^{2}-16$

Accepted Answer

A)  $\left(r^{2}+4\right)\left(s^{2}-4\right)$ 
B)  $(\mathrm{r}-\mathrm{s}+4)(\mathrm{r}-\mathrm{s}-4)$ 
C)  $(\mathrm{r}+\mathrm{s}+4)(\mathrm{r}-\mathrm{s}-4)$ 
D)  $(\mathrm{r}+\mathrm{s}+4)(\mathrm{r}+\mathrm{s}-4)$ 
A)  $\left(r^{2}+4\right)\left(s^{2}-4\right)$ 
B)  $(\mathrm{r}-\mathrm{s}+4)(\mathrm{r}-\mathrm{s}-4)$ 
C)  $(\mathrm{r}+\mathrm{s}+4)(\mathrm{r}-\mathrm{s}-4)$ 
D)  $(\mathrm{r}+\mathrm{s}+4)(\mathrm{r}+\mathrm{s}-4)$

Question 8

Factor the polynomial completely
-$16 m^{4}-24 m^{3}+54 m p^{3}-81 p^{3}$

Accepted Answer

A)  $8 m^{3}(2 m-3)+27 p^{3}(2 m-3)$ 
B)  $\left(4 m^{2}-6 m+6 m p-9 p\right)\left(4 m^{2}+6 m p+4 p^{2}\right)$ 
C)  $16 m^{4}-24 m^{3}-54 m p^{3}+81 p^{3}$ 
D)  $(2 m+3 p)(2 m-3)\left(4 m^{2}-6 m p+9 p^{2}\right)$ 
A)  $8 m^{3}(2 m-3)+27 p^{3}(2 m-3)$ 
B)  $\left(4 m^{2}-6 m+6 m p-9 p\right)\left(4 m^{2}+6 m p+4 p^{2}\right)$ 
C)  $16 m^{4}-24 m^{3}-54 m p^{3}+81 p^{3}$ 
D)  $(2 m+3 p)(2 m-3)\left(4 m^{2}-6 m p+9 p^{2}\right)$

Question 9

Factor the trinomial completely.
-$-49 x^{2}-14 x+15$

Accepted Answer

A)  $(7 x+5)(7 x+3)$ 
B)  $-(7 x-5)(7 x+3)$ 
C)  $-(7 x-5)(7 x-3)$ 
D)  $-(7 x+5)(7 x-3)$ 
A)  $(7 x+5)(7 x+3)$ 
B)  $-(7 x-5)(7 x+3)$ 
C)  $-(7 x-5)(7 x-3)$ 
D)  $-(7 x+5)(7 x-3)$

Question 10

Factor the polynomial $5 a^{4}+34 a^{2}-7$. Explain the method used.

Accepted Answer

The polynomial @#LAT-DLM& is factored co

Question 11

Factor the polynomial completely
-$50 a^{4}-98 b^{2}$

Accepted Answer

A)  $2\left(5 a^{2}-7 b\right)^{2}$ 
B)  $2\left(5 a^{2}+7 b\right)\left(5 a^{2}-7 b\right)$ 
C)  $2\left(5 a^{2}+7 b\right)^{2}$ 
D)  $\left(10 a^{2}+14 b\right)\left(5 a^{2}-7 b\right)$ 
A)  $2\left(5 a^{2}-7 b\right)^{2}$ 
B)  $2\left(5 a^{2}+7 b\right)\left(5 a^{2}-7 b\right)$ 
C)  $2\left(5 a^{2}+7 b\right)^{2}$ 
D)  $\left(10 a^{2}+14 b\right)\left(5 a^{2}-7 b\right)$

Question 12

Solve the equation for the specified variable.
-$w=\frac{7 y-x}{y}$ for $y$

Accepted Answer

A)  $y=\frac{-x}{w-7}$ or $y=\frac{x}{7-w}$ 
B)  $y=\frac{w-7}{-x}$ or $y=\frac{7-w}{x}$ 
C)  $y=\frac{x}{w-7}$ or $y=\frac{-x}{7-w}$ 
D)  $y=\frac{7-x}{w}$ or $y=\frac{x-7}{-w}$ 
A)  $y=\frac{-x}{w-7}$ or $y=\frac{x}{7-w}$ 
B)  $y=\frac{w-7}{-x}$ or $y=\frac{7-w}{x}$ 
C)  $y=\frac{x}{w-7}$ or $y=\frac{-x}{7-w}$ 
D)  $y=\frac{7-x}{w}$ or $y=\frac{x-7}{-w}$

Question 13

actor out the greatest common factor. Simplify the factors, if possible
-$2 x^{3}+6 x$

Accepted Answer

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

Question 14

Factor the polynomial completely
-$4 x^{6}-25$

Accepted Answer

A)  $\left(2 x^{3}-5\right)^{2}$ 
B)  $\left(2 x^{3}+5\right)^{2}$ 
C)  $4 x^{6}-25$ 
D)  $\left(2 x^{3}-5\right)\left(2 x^{3}+5\right)$ 
A)  $\left(2 x^{3}-5\right)^{2}$ 
B)  $\left(2 x^{3}+5\right)^{2}$ 
C)  $4 x^{6}-25$ 
D)  $\left(2 x^{3}-5\right)\left(2 x^{3}+5\right)$

Question 15

Factor the polynomial completely
-$(x-2 y)^{2}-49$

Accepted Answer

A)  $(x+2 y+7)(x-2 y-7)$ 
B)  $(x-2 y+49)(x-2 y-49)$ 
C)  $\left(x^{2}-2 y+7\right)\left(x^{2}-2 y-7\right)$ 
D)  $(x-2 y+7)(x-2 y-7)$ 
A)  $(x+2 y+7)(x-2 y-7)$ 
B)  $(x-2 y+49)(x-2 y-49)$ 
C)  $\left(x^{2}-2 y+7\right)\left(x^{2}-2 y-7\right)$ 
D)  $(x-2 y+7)(x-2 y-7)$

Question 16

Decide if the expression is factored
-$3 \mathrm{k}(5 \mathrm{k}-\mathrm{p})$

Accepted Answer

A) True 
 B)False

Question 17

Factor the trinomial completely.
-$60 z^{8}-56 z^{5}-32 z^{2}$

Accepted Answer

A)  $4 z^{2}\left(5 z^{3}-2\right)\left(3 z^{3}+4\right)$ 
B)  $4\left(3 z^{6}-4\right)\left(5 z^{2}+2\right)$ 
C)  $4 z^{2}\left(3 z^{3}-4\right)\left(5 z^{3}+2\right)$ 
D)  $\left(3 z^{4}+3\right)\left(5 z^{4}+2\right)$ 
A)  $4 z^{2}\left(5 z^{3}-2\right)\left(3 z^{3}+4\right)$ 
B)  $4\left(3 z^{6}-4\right)\left(5 z^{2}+2\right)$ 
C)  $4 z^{2}\left(3 z^{3}-4\right)\left(5 z^{3}+2\right)$ 
D)  $\left(3 z^{4}+3\right)\left(5 z^{4}+2\right)$

Question 18

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

Accepted Answer

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

Question 19

$3 x^{2}+17 x=-20$

Accepted Answer

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

Question 20

Factor the polynomial completely
-$x^{3}-512$

Accepted Answer

A)  $(x-8)\left(x^{2}+64\right)$ 
B)  $(x-8)\left(x^{2}+8 x+64\right)$ 
C)  $(x+8)\left(x^{2}-8 x+64\right)$ 
D)  $(x+512)\left(x^{2}-1\right)$ 
A)  $(x-8)\left(x^{2}+64\right)$ 
B)  $(x-8)\left(x^{2}+8 x+64\right)$ 
C)  $(x+8)\left(x^{2}-8 x+64\right)$ 
D)  $(x+512)\left(x^{2}-1\right)$

$6 x^{2}-7 x-24$

A farmer has 260 meters of fencing and wants to enclose a rectangular area of 3600 square meters. What dimensions should he use?

Factor by grouping. -11) $7 y+7 a-y^{2}-y a$

Factor the polynomial completely - $1-1296 \mathrm{~m}^{4}$

Factor the polynomial completely - $40 x^{3}+14 x^{2}-12 x$

Factor by grouping. - $x^{3}+4 x^{2}+2 x+8$

Factor the polynomial - $r^{2}+2 r s+s^{2}-16$

Factor the polynomial completely - $16 m^{4}-24 m^{3}+54 m p^{3}-81 p^{3}$

Factor the trinomial completely. - $-49 x^{2}-14 x+15$

Factor the polynomial $5 a^{4}+34 a^{2}-7$ . Explain the method used.

Factor the polynomial completely - $50 a^{4}-98 b^{2}$

Solve the equation for the specified variable. - $w=\frac{7 y-x}{y}$ for $y$

actor out the greatest common factor. Simplify the factors, if possible - $2 x^{3}+6 x$

Factor the polynomial completely - $4 x^{6}-25$

Factor the polynomial completely - $(x-2 y)^{2}-49$

Decide if the expression is factored - $3 \mathrm{k}(5 \mathrm{k}-\mathrm{p})$

Factor the trinomial completely. - $60 z^{8}-56 z^{5}-32 z^{2}$

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

$3 x^{2}+17 x=-20$

Factor the polynomial completely - $x^{3}-512$

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

6x2−7x−246 x^{2}-7 x-246x2−7x−24

A farmer has 260 meters of fencing and wants to enclose a rectangular area of 3600 square meters. What dimensions should he use?

Factor by grouping. -11) 7y+7a−y2−ya7 y+7 a-y^{2}-y a7y+7a−y2−ya

Factor the polynomial completely - 1−1296 m41-1296 \mathrm{~m}^{4}1−1296 m4

Factor the polynomial completely - 40x3+14x2−12x40 x^{3}+14 x^{2}-12 x40x3+14x2−12x

Factor by grouping. - x3+4x2+2x+8x^{3}+4 x^{2}+2 x+8x3+4x2+2x+8

Factor the polynomial - r2+2rs+s2−16r^{2}+2 r s+s^{2}-16r2+2rs+s2−16

Factor the polynomial completely - 16m4−24m3+54mp3−81p316 m^{4}-24 m^{3}+54 m p^{3}-81 p^{3}16m4−24m3+54mp3−81p3

Factor the trinomial completely. - −49x2−14x+15-49 x^{2}-14 x+15−49x2−14x+15

Factor the polynomial 5a4+34a2−75 a^{4}+34 a^{2}-75a4+34a2−7 . Explain the method used.

Factor the polynomial completely - 50a4−98b250 a^{4}-98 b^{2}50a4−98b2

Solve the equation for the specified variable. - w=7y−xyw=\frac{7 y-x}{y}w=y7y−x​ for yyy

actor out the greatest common factor. Simplify the factors, if possible - 2x3+6x2 x^{3}+6 x2x3+6x

Factor the polynomial completely - 4x6−254 x^{6}-254x6−25

Factor the polynomial completely - (x−2y)2−49(x-2 y)^{2}-49(x−2y)2−49

Decide if the expression is factored - 3k(5k−p)3 \mathrm{k}(5 \mathrm{k}-\mathrm{p})3k(5k−p)

Factor the trinomial completely. - 60z8−56z5−32z260 z^{8}-56 z^{5}-32 z^{2}60z8−56z5−32z2

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

3x2+17x=−203 x^{2}+17 x=-203x2+17x=−20

Factor the polynomial completely - x3−512x^{3}-512x3−512

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

$6 x^{2}-7 x-24$

Factor by grouping. -11) $7 y+7 a-y^{2}-y a$

Factor the polynomial completely - $1-1296 \mathrm{~m}^{4}$

Factor the polynomial completely - $40 x^{3}+14 x^{2}-12 x$

Factor by grouping. - $x^{3}+4 x^{2}+2 x+8$

Factor the polynomial - $r^{2}+2 r s+s^{2}-16$

Factor the polynomial completely - $16 m^{4}-24 m^{3}+54 m p^{3}-81 p^{3}$

Factor the trinomial completely. - $-49 x^{2}-14 x+15$

Factor the polynomial $5 a^{4}+34 a^{2}-7$ . Explain the method used.

Factor the polynomial completely - $50 a^{4}-98 b^{2}$

Solve the equation for the specified variable. - $w=\frac{7 y-x}{y}$ for $y$

actor out the greatest common factor. Simplify the factors, if possible - $2 x^{3}+6 x$

Factor the polynomial completely - $4 x^{6}-25$

Factor the polynomial completely - $(x-2 y)^{2}-49$

Decide if the expression is factored - $3 \mathrm{k}(5 \mathrm{k}-\mathrm{p})$

Factor the trinomial completely. - $60 z^{8}-56 z^{5}-32 z^{2}$

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

$3 x^{2}+17 x=-20$

Factor the polynomial completely - $x^{3}-512$