Question 1

Factor completely.
-$50 x^{2}-8 y^{2}$

Accepted Answer

A)  $(5 x+2 y)(10 x-4 y)$ 
B)  $2(5 \mathrm{x}+2 \mathrm{y})(5 \mathrm{x}-2 \mathrm{y})$ 
C)  $(10 x+4 y)(5 x-2 y)$ 
D)  $2(5 x-2 y)^{2}$ 
A)  $(5 x+2 y)(10 x-4 y)$ 
B)  $2(5 \mathrm{x}+2 \mathrm{y})(5 \mathrm{x}-2 \mathrm{y})$ 
C)  $(10 x+4 y)(5 x-2 y)$ 
D)  $2(5 x-2 y)^{2}$

Question 2

Factor.
-$10 x^{2}-35 x-20$

Accepted Answer

A)  $5(2 x-1)(x+4)$ 
B)  $(2 x-1)(5 x+20)$ 
C)  $(10 x-5)(x+4)$ 
D)  $5(2 x+1)(x-4)$ 
A)  $5(2 x-1)(x+4)$ 
B)  $(2 x-1)(5 x+20)$ 
C)  $(10 x-5)(x+4)$ 
D)  $5(2 x+1)(x-4)$

Question 3

Solve the problem.
-The product of two consecutive integers is 8 less than 8 times their sum. Find the integers.

Accepted Answer

A)  15,16 
B)  0,1 or 15,16 
C)  0,1 or 16,17 
D)  0,1 
A)  15,16 
B)  0,1 or 15,16 
C)  0,1 or 16,17 
D)  0,1

Question 4

Factor.
-$3 x^{2} y^{6}+21 x^{2} y^{5}$

Accepted Answer

A)  $3 x^{5} y^{2}(y+7)$ 
B)  $3 x^{2} y^{5}(y+7)$ 
C)  $y+7$ 
D)  $x^{2} y^{5}(3 y+7)$ 
A)  $3 x^{5} y^{2}(y+7)$ 
B)  $3 x^{2} y^{5}(y+7)$ 
C)  $y+7$ 
D)  $x^{2} y^{5}(3 y+7)$

Question 5

Factor completely.
-$20 x^{3}-12 x^{2} y-25 x y+15 y^{2}$

Accepted Answer

A)  $\left(20 x^{2}-5 y\right)(x-3 y)$ 
B)  $\left(4 x^{2}-5\right)(5 x-3)$ 
C)  $\left(4 x^{2}-5 y\right)(5 x-3 y)$ 
D)  $\left(4 x^{2}+5 y\right)(5 x-3 y)$ 
A)  $\left(20 x^{2}-5 y\right)(x-3 y)$ 
B)  $\left(4 x^{2}-5\right)(5 x-3)$ 
C)  $\left(4 x^{2}-5 y\right)(5 x-3 y)$ 
D)  $\left(4 x^{2}+5 y\right)(5 x-3 y)$

Question 6

Factor.
-$24 z^{6}+52 z^{4}+24 z^{2}$

Accepted Answer

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

Question 7

Solve using the principle of zero products.
-$x\left(5 x-\frac{1}{2}\right)\left(x+\frac{1}{5}\right)=0$

Accepted Answer

A)  $0,-\frac{1}{10},-\frac{1}{5}$ 
B)  $0, \frac{1}{10},-\frac{1}{5}$ 
C)  $0, \frac{1}{10}, \frac{1}{5}$ 
D)  $0,-\frac{1}{10}, \frac{1}{5}$ 
A)  $0,-\frac{1}{10},-\frac{1}{5}$ 
B)  $0, \frac{1}{10},-\frac{1}{5}$ 
C)  $0, \frac{1}{10}, \frac{1}{5}$ 
D)  $0,-\frac{1}{10}, \frac{1}{5}$

Question 8

Provide an appropriate response.
-Explain the error in the following:
$$x^{2}-y^{2}=(x-y)^{2}$$

Accepted Answer

@#LAT-DLM& is a difference of

Question 9

Solve using the principle of zero products.
-$\left(3 \mathrm{x}-\frac{1}{2}\right)\left(\mathrm{x}+\frac{1}{3}\right)=0$

Accepted Answer

A)  $-\frac{1}{6}, \frac{1}{3}$ 
B)  $\frac{1}{6},-\frac{1}{3}$ 
C)  $-\frac{1}{6},-\frac{1}{3}$ 
D)  $\frac{1}{6}, \frac{1}{3}$ 
A)  $-\frac{1}{6}, \frac{1}{3}$ 
B)  $\frac{1}{6},-\frac{1}{3}$ 
C)  $-\frac{1}{6},-\frac{1}{3}$ 
D)  $\frac{1}{6}, \frac{1}{3}$

Question 10

Factor using the ac-method.
-$9-6 x+x^{2}$

Accepted Answer

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

Question 11

Factor.
-$x^{3}+5 x^{2}-84 x$

Accepted Answer

A)  $\left(x^{2}+12\right)(x-7)$ 
B)  $\left(x^{2}+7\right)(x-12)$ 
C)  $x(x+12)(x-7)$ 
D)  $x(x-12)(x+7)$ 
A)  $\left(x^{2}+12\right)(x-7)$ 
B)  $\left(x^{2}+7\right)(x-12)$ 
C)  $x(x+12)(x-7)$ 
D)  $x(x-12)(x+7)$

Question 12

Factor completely.
-$9 x^{2}+12 x+4$

Accepted Answer

A)  $(3 x+2)(3 x-2)$ 
B)  $(3 \mathrm{x}-2)^{2}$ 
C)  $(3 x+2)^{2}$ 
D)  Prime 
A)  $(3 x+2)(3 x-2)$ 
B)  $(3 \mathrm{x}-2)^{2}$ 
C)  $(3 x+2)^{2}$ 
D)  Prime

Question 13

Solve by factoring and using the principle of zero products.
-$\mathrm{x}^{2}+2 \mathrm{x}-120=0$

Accepted Answer

A)  12,10 
B)  $12,-10$ 
C)  $-12,10$ 
D)  $-12,1$ 
A)  12,10 
B)  $12,-10$ 
C)  $-12,10$ 
D)  $-12,1$

Question 14

Factor completely.
-$6 x^{2}-21 x-12$

Accepted Answer

A)  $(2 x-1)(3 x+12)$ 
B)  $3(2 x-1)(x+4)$ 
C)  $(6 x-3)(x+4)$ 
D)  $3(2 x+1)(x-4)$ 
A)  $(2 x-1)(3 x+12)$ 
B)  $3(2 x-1)(x+4)$ 
C)  $(6 x-3)(x+4)$ 
D)  $3(2 x+1)(x-4)$

Question 15

Factor.
-$4 x^{2}-7 x+8$

Accepted Answer

A)  Prime 
B)  $(2 x-8)(2 x-1)$ 
C)  $(4 \mathrm{x}-1)(\mathrm{x}-8)$ 
D)  $(4 x-8)(x-1)$ 
A)  Prime 
B)  $(2 x-8)(2 x-1)$ 
C)  $(4 \mathrm{x}-1)(\mathrm{x}-8)$ 
D)  $(4 x-8)(x-1)$

Question 16

Factor by grouping.
-$x^{3}+2 x^{2}-6 x-12$

Accepted Answer

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

Question 17

Factor.
-$x^{2}+\frac{6}{7} x+\frac{9}{49}$

Accepted Answer

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

Question 18

Find the $x$-intercepts of the graph of the equation. (The grids are intentionally not included.)
-$y=x^{2}-x-12$

Accepted Answer

A)  $(-3,0),(4,0)$ 
B)  $(4,0),(3,0)$ 
C)  $(12,0)$ 
D)  $(1,0),(-12,0)$ 
A)  $(-3,0),(4,0)$ 
B)  $(4,0),(3,0)$ 
C)  $(12,0)$ 
D)  $(1,0),(-12,0)$

Question 19

Factor completely.
-$294 x^{2}-6$

Accepted Answer

A)  $6(7 x+1)^{2}$ 
B)  $(7 x-1)(42 x+6)$ 
C)  $6(7 x-1)(7 x+1)$ 
D)  $(42 \mathrm{x}-6)(7 \mathrm{x}+1)$ 
A)  $6(7 x+1)^{2}$ 
B)  $(7 x-1)(42 x+6)$ 
C)  $6(7 x-1)(7 x+1)$ 
D)  $(42 \mathrm{x}-6)(7 \mathrm{x}+1)$

Question 20

Factor.
-$x^{2}+3 x y-130 y^{2}$

Accepted Answer

A)  $(x-13 y)(x+y)$ 
B)  $(x-13 y)(x+10 y)$ 
C)  $(x+13 y)(x-10 y)$ 
D)  $(x-y)(x+10 y)$ 
A)  $(x-13 y)(x+y)$ 
B)  $(x-13 y)(x+10 y)$ 
C)  $(x+13 y)(x-10 y)$ 
D)  $(x-y)(x+10 y)$

Factor completely. - $50 x^{2}-8 y^{2}$

Factor. - $10 x^{2}-35 x-20$

Solve the problem. -The product of two consecutive integers is 8 less than 8 times their sum. Find the integers.

Factor. - $3 x^{2} y^{6}+21 x^{2} y^{5}$

Factor completely. - $20 x^{3}-12 x^{2} y-25 x y+15 y^{2}$

Factor. - $24 z^{6}+52 z^{4}+24 z^{2}$

Solve using the principle of zero products. - $x\left(5 x-\frac{1}{2}\right)\left(x+\frac{1}{5}\right)=0$

Provide an appropriate response. -Explain the error in the following: $x^{2}-y^{2}=(x-y)^{2}$

Solve using the principle of zero products. - $\left(3 \mathrm{x}-\frac{1}{2}\right)\left(\mathrm{x}+\frac{1}{3}\right)=0$

Factor using the ac-method. - $9-6 x+x^{2}$

Factor. - $x^{3}+5 x^{2}-84 x$

Factor completely. - $9 x^{2}+12 x+4$

Solve by factoring and using the principle of zero products. - $\mathrm{x}^{2}+2 \mathrm{x}-120=0$

Factor completely. - $6 x^{2}-21 x-12$

Factor. - $4 x^{2}-7 x+8$

Factor by grouping. - $x^{3}+2 x^{2}-6 x-12$

Factor. - $x^{2}+\frac{6}{7} x+\frac{9}{49}$

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=x^{2}-x-12$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=x^{2}-x-12$

Factor completely. - $294 x^{2}-6$

Factor. - $x^{2}+3 x y-130 y^{2}$

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

Equations of Lines and Simplifying Radical Expressions

Filters

Exam 5: Polynomials: Factoring

Factor completely. - 50x2−8y250 x^{2}-8 y^{2}50x2−8y2

Factor. - 10x2−35x−2010 x^{2}-35 x-2010x2−35x−20

Solve the problem. -The product of two consecutive integers is 8 less than 8 times their sum. Find the integers.

Factor. - 3x2y6+21x2y53 x^{2} y^{6}+21 x^{2} y^{5}3x2y6+21x2y5

Factor completely. - 20x3−12x2y−25xy+15y220 x^{3}-12 x^{2} y-25 x y+15 y^{2}20x3−12x2y−25xy+15y2

Factor. - 24z6+52z4+24z224 z^{6}+52 z^{4}+24 z^{2}24z6+52z4+24z2

Solve using the principle of zero products. - x(5x−12)(x+15)=0x\left(5 x-\frac{1}{2}\right)\left(x+\frac{1}{5}\right)=0x(5x−21​)(x+51​)=0

Provide an appropriate response. -Explain the error in the following: x2−y2=(x−y)2x^{2}-y^{2}=(x-y)^{2}x2−y2=(x−y)2

Solve using the principle of zero products. - (3x−12)(x+13)=0\left(3 \mathrm{x}-\frac{1}{2}\right)\left(\mathrm{x}+\frac{1}{3}\right)=0(3x−21​)(x+31​)=0

Factor using the ac-method. - 9−6x+x29-6 x+x^{2}9−6x+x2

Factor. - x3+5x2−84xx^{3}+5 x^{2}-84 xx3+5x2−84x

Factor completely. - 9x2+12x+49 x^{2}+12 x+49x2+12x+4

Solve by factoring and using the principle of zero products. - x2+2x−120=0\mathrm{x}^{2}+2 \mathrm{x}-120=0x2+2x−120=0

Factor completely. - 6x2−21x−126 x^{2}-21 x-126x2−21x−12

Factor. - 4x2−7x+84 x^{2}-7 x+84x2−7x+8

Factor by grouping. - x3+2x2−6x−12x^{3}+2 x^{2}-6 x-12x3+2x2−6x−12

Factor. - x2+67x+949x^{2}+\frac{6}{7} x+\frac{9}{49}x2+76​x+499​

Find the xxx -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=x2−x−12y=x^{2}-x-12y=x2−x−12

Factor completely. - 294x2−6294 x^{2}-6294x2−6

Factor. - x2+3xy−130y2x^{2}+3 x y-130 y^{2}x2+3xy−130y2