Question 1

Factor completely.
-$25 x^{2} y^{2}-70 x y+49$

Accepted Answer

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

Question 2

Solve by factoring and using the principle of zero products.
-$24 n^{2}+20 n=0$

Accepted Answer

A)  0 
B)  $-\frac{5}{6}, 0$ 
C)  $-\frac{5}{6}$ 
D)  $-\frac{5}{6}, 20$ 
A)  0 
B)  $-\frac{5}{6}, 0$ 
C)  $-\frac{5}{6}$ 
D)  $-\frac{5}{6}, 20$

Question 3

Factor completely.
-$5 x^{8}-1280$

Accepted Answer

A)  $5\left(x^{4}+16\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
B)  $5\left(x^{4}-16\right)^{2}$ 
C)  $\left(5 x^{4}+80\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
D)  $5\left(x^{4}+16\right)\left(x^{4}-16\right)$ 
A)  $5\left(x^{4}+16\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
B)  $5\left(x^{4}-16\right)^{2}$ 
C)  $\left(5 x^{4}+80\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
D)  $5\left(x^{4}+16\right)\left(x^{4}-16\right)$

Question 4

Factor completely.
-$x^{3}+3 x^{2}-36 x-108$

Accepted Answer

A)  $(x+6)(x-6)(x-3)$ 
B)  $\left(x^{2}+36\right)(x-3)$ 
C)  $(x+6)(x-6)(x+3)$ 
D)  $x(x-36)(x+3)$ 
A)  $(x+6)(x-6)(x-3)$ 
B)  $\left(x^{2}+36\right)(x-3)$ 
C)  $(x+6)(x-6)(x+3)$ 
D)  $x(x-36)(x+3)$

Question 5

Factor by grouping.
-$12 x^{2}+10 x y+18 x y+15 y^{2}$

Accepted Answer

A)  $(2 x-3 y)(6 x+5 y)$ 
B)  $(2 x+3 y)(6 x+5 y)$ 
C)  $(2 x+3)(6 x+5)$ 
D)  $(12 x+3 y)(x+5 y)$ 
A)  $(2 x-3 y)(6 x+5 y)$ 
B)  $(2 x+3 y)(6 x+5 y)$ 
C)  $(2 x+3)(6 x+5)$ 
D)  $(12 x+3 y)(x+5 y)$

Question 6

Factor completely.
-$10 x^{3}-15 x^{2} y+12 x y-18 y^{2}$

Accepted Answer

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

Question 7

Factor by grouping.
-$2 x^{3}-10 x^{2}-3 x+15$

Accepted Answer

A)  $(x+15)\left(x^{2}-10 x-3\right)$ 
B)  $(x-5)\left(2 x^{2}-3\right)$ 
C)  Not possible 
D)  $(x+5)\left(2 x^{2}-3\right)$ 
A)  $(x+15)\left(x^{2}-10 x-3\right)$ 
B)  $(x-5)\left(2 x^{2}-3\right)$ 
C)  Not possible 
D)  $(x+5)\left(2 x^{2}-3\right)$

Question 8

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

Accepted Answer

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

Question 9

Determine whether the following is a difference of squares.
-$x^{2}-81 y^{2}$

Accepted Answer

A) True 
 B)False

Question 10

Factor using the ac-method.
-$9 x^{2}-3 x t-2 t^{2}$

Accepted Answer

A)  $(3 x-t)(3 x+2 t)$ 
B)  $(3 x+t)(3 x-2 t)$ 
C)  prime 
D)  $(9 x+t)(x-2 t)$ 
A)  $(3 x-t)(3 x+2 t)$ 
B)  $(3 x+t)(3 x-2 t)$ 
C)  prime 
D)  $(9 x+t)(x-2 t)$

Question 11

Factor.
-$5 x^{9}-50 x^{8}-105 x^{7}$

Accepted Answer

A)  $5 x^{7}\left(x^{2}-6 x-21\right)$ 
B)  $5 x^{6}\left(x^{2}-6 x-21\right)$ 
C)  $5 x^{7}(x-7)(x-3)$ 
D)  $5 x^{7}(x-7)(x+3)$ 
A)  $5 x^{7}\left(x^{2}-6 x-21\right)$ 
B)  $5 x^{6}\left(x^{2}-6 x-21\right)$ 
C)  $5 x^{7}(x-7)(x-3)$ 
D)  $5 x^{7}(x-7)(x+3)$

Question 12

Factor.
-$4 x^{2}-28 x+48$

Accepted Answer

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

Question 13

Factor.
-$u^{2}-5 u v-50 v^{2}$

Accepted Answer

A)  $(u+5 v)(u-10 v)$ 
B)  $(u-v)(u+10 v)$ 
C)  $(u-5 v)(u+10 v)$ 
D)  $(u-5 v)(u+v)$ 
A)  $(u+5 v)(u-10 v)$ 
B)  $(u-v)(u+10 v)$ 
C)  $(u-5 v)(u+10 v)$ 
D)  $(u-5 v)(u+v)$

Question 14

Factor.
-$2 y+8$

Accepted Answer

A)  8 
B)  No common factor 
C)  $2 y$ 
D)  $2(y+4)$ 
A)  8 
B)  No common factor 
C)  $2 y$ 
D)  $2(y+4)$

Question 15

Solve.
-Use the following graph to solve $x^{2}-2 x-3=0$.
$y=x^{2}-2 x-3$

Accepted Answer

A)  $-1,3$ 
B)  3,1 
C)  $-3,-1$ 
D)  $-3,1$ 
A)  $-1,3$ 
B)  3,1 
C)  $-3,-1$ 
D)  $-3,1$

Question 16

Determine whether the following is a difference of squares.
-$x^{2}-14$

Accepted Answer

A) True 
 B)False

Question 17

Solve the problem.
-The height of a box is 6 inches. The length is three inches more than the width. Find the width if the volume is 240 cubic inches.

Accepted Answer

A)  6 in. 
B)  5 in. 
C)  8 in. 
D)  $40 \mathrm{in}$. 
A)  6 in. 
B)  5 in. 
C)  8 in. 
D)  $40 \mathrm{in}$.

Question 18

Factor.
-$w^{7}-29 w a^{6}+7 w^{3} a^{7}-3 w^{7} a^{6}$

Accepted Answer

A)  $w a^{6}\left(w^{6}-29+7 w^{2} a^{1}-3 w^{6}\right)$ 
B)  $w a\left(w^{6}-29 a^{5}+7 w^{2} a^{6}-3 w^{6} a^{5}\right)$ 
C)  $w^{2}\left(w^{6}-29 a^{5}+7 w^{2} a^{6}-3 w^{6} a^{5}\right)$ 
D)  $w\left(w^{6}-29 a^{6}+7 w^{2} a^{7}-3 w^{6} a^{6}\right)$ 
A)  $w a^{6}\left(w^{6}-29+7 w^{2} a^{1}-3 w^{6}\right)$ 
B)  $w a\left(w^{6}-29 a^{5}+7 w^{2} a^{6}-3 w^{6} a^{5}\right)$ 
C)  $w^{2}\left(w^{6}-29 a^{5}+7 w^{2} a^{6}-3 w^{6} a^{5}\right)$ 
D)  $w\left(w^{6}-29 a^{6}+7 w^{2} a^{7}-3 w^{6} a^{6}\right)$

Question 19

Solve using the principle of zero products.
-$(x-6)(x+79)(10 x+14)=0$

Accepted Answer

A)  $6,-79,-140$ 
B)  $6,-79,-\frac{5}{7}$ 
C)  $-6,79, \frac{7}{5}$ 
D)  $6,-79,-\frac{7}{5}$ 
A)  $6,-79,-140$ 
B)  $6,-79,-\frac{5}{7}$ 
C)  $-6,79, \frac{7}{5}$ 
D)  $6,-79,-\frac{7}{5}$

Question 20

Factor.
-$\mathrm{p}^{4}-11 \mathrm{p}^{2}+24$

Accepted Answer

A)  $\left(p^{2}-3\right)\left(p^{2}-8\right)$ 
B)  $p^{2}(p-3)(p-8)$ 
C)  $\left(\mathrm{p}^{2}-3\right)\left(\mathrm{p}^{2}+8\right)$ 
D)  $\left(p^{2}-24\right)\left(p^{2}-1\right)$ 
A)  $\left(p^{2}-3\right)\left(p^{2}-8\right)$ 
B)  $p^{2}(p-3)(p-8)$ 
C)  $\left(\mathrm{p}^{2}-3\right)\left(\mathrm{p}^{2}+8\right)$ 
D)  $\left(p^{2}-24\right)\left(p^{2}-1\right)$

Factor completely. - $25 x^{2} y^{2}-70 x y+49$

Solve by factoring and using the principle of zero products. - $24 n^{2}+20 n=0$

Factor completely. - $5 x^{8}-1280$

Factor completely. - $x^{3}+3 x^{2}-36 x-108$

Factor by grouping. - $12 x^{2}+10 x y+18 x y+15 y^{2}$

Factor completely. - $10 x^{3}-15 x^{2} y+12 x y-18 y^{2}$

Factor by grouping. - $2 x^{3}-10 x^{2}-3 x+15$

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

Determine whether the following is a difference of squares. - $x^{2}-81 y^{2}$

Factor using the ac-method. - $9 x^{2}-3 x t-2 t^{2}$

Factor. - $5 x^{9}-50 x^{8}-105 x^{7}$

Factor. - $4 x^{2}-28 x+48$

Factor. - $u^{2}-5 u v-50 v^{2}$

Factor. - $2 y+8$

Solve. -Use the following graph to solve $x^{2}-2 x-3=0$ . $y=x^{2}-2 x-3$ $Solve. -Use the following graph to solve x^{2}-2 x-3=0 . y=x^{2}-2 x-3$

Determine whether the following is a difference of squares. - $x^{2}-14$

Solve the problem. -The height of a box is 6 inches. The length is three inches more than the width. Find the width if the volume is 240 cubic inches.

Factor. - $w^{7}-29 w a^{6}+7 w^{3} a^{7}-3 w^{7} a^{6}$

Solve using the principle of zero products. - $(x-6)(x+79)(10 x+14)=0$

Factor. - $\mathrm{p}^{4}-11 \mathrm{p}^{2}+24$

Whole Numbers

Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Converting Units of Measurement

Filters

Exam 11: Polynomials: Factoring

Factor completely. - 25x2y2−70xy+4925 x^{2} y^{2}-70 x y+4925x2y2−70xy+49

Solve by factoring and using the principle of zero products. - 24n2+20n=024 n^{2}+20 n=024n2+20n=0

Factor completely. - 5x8−12805 x^{8}-12805x8−1280

Factor completely. - x3+3x2−36x−108x^{3}+3 x^{2}-36 x-108x3+3x2−36x−108

Factor by grouping. - 12x2+10xy+18xy+15y212 x^{2}+10 x y+18 x y+15 y^{2}12x2+10xy+18xy+15y2

Factor completely. - 10x3−15x2y+12xy−18y210 x^{3}-15 x^{2} y+12 x y-18 y^{2}10x3−15x2y+12xy−18y2

Factor by grouping. - 2x3−10x2−3x+152 x^{3}-10 x^{2}-3 x+152x3−10x2−3x+15

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

Determine whether the following is a difference of squares. - x2−81y2x^{2}-81 y^{2}x2−81y2

Factor using the ac-method. - 9x2−3xt−2t29 x^{2}-3 x t-2 t^{2}9x2−3xt−2t2

Factor. - 5x9−50x8−105x75 x^{9}-50 x^{8}-105 x^{7}5x9−50x8−105x7

Factor. - 4x2−28x+484 x^{2}-28 x+484x2−28x+48

Factor. - u2−5uv−50v2u^{2}-5 u v-50 v^{2}u2−5uv−50v2

Factor. - 2y+82 y+82y+8

Solve. -Use the following graph to solve x2−2x−3=0x^{2}-2 x-3=0x2−2x−3=0 . y=x2−2x−3y=x^{2}-2 x-3y=x2−2x−3

Determine whether the following is a difference of squares. - x2−14x^{2}-14x2−14