Question 1

Solve using the principle of zero products.
-$(x-0.4)(x+0.3)=0$

Accepted Answer

A)  $0.4,0.3$ 
B)  $0.4,-0.3$ 
C)  $-0.4,0.3$ 
D)  $0.4,-0.4,0.3,-0.3$ 
A)  $0.4,0.3$ 
B)  $0.4,-0.3$ 
C)  $-0.4,0.3$ 
D)  $0.4,-0.4,0.3,-0.3$

Question 2

Factor.
-$x^{2}-x-42$

Accepted Answer

A)  $(x+6)(x-7)$ 
B)  $(x+1)(x-42)$ 
C)  Prime 
D)  $(x+7)(x-6)$ 
A)  $(x+6)(x-7)$ 
B)  $(x+1)(x-42)$ 
C)  Prime 
D)  $(x+7)(x-6)$

Question 3

Determine whether the following is a trinomial square.
-$21 x^{2}-91 x-70$

Accepted Answer

A) True 
 B)False

Question 4

Determine whether the following is a difference of squares.
-$22 x^{2}-y^{2}$

Accepted Answer

A) True 
 B)False

Question 5

Factor using the ac-method.
-$10 x^{4}+23 x^{2}+12$

Accepted Answer

A)  $\left(2 x^{2}+1\right)\left(5 x^{2}+12\right)$ 
B)  $\left(5 x^{2}-4\right)\left(2 x^{2}-3\right)$ 
C)  $\left(10 x^{2}+3\right)\left(x^{2}+4\right)$ 
D)  $\left(2 x^{2}+3\right)\left(5 x^{2}+4\right)$ 
A)  $\left(2 x^{2}+1\right)\left(5 x^{2}+12\right)$ 
B)  $\left(5 x^{2}-4\right)\left(2 x^{2}-3\right)$ 
C)  $\left(10 x^{2}+3\right)\left(x^{2}+4\right)$ 
D)  $\left(2 x^{2}+3\right)\left(5 x^{2}+4\right)$

Question 6

Factor completely.
-$121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}$

Accepted Answer

A)  Prime 
B)  $(11 \mathrm{k}+7 \mathrm{~m})(11 \mathrm{k}-7 \mathrm{~m})$ 
C)  $(11 \mathrm{k}+7 \mathrm{~m})^{2}$ 
D)  $(11 \mathrm{k}-7 \mathrm{~m})^{2}$ 
A)  Prime 
B)  $(11 \mathrm{k}+7 \mathrm{~m})(11 \mathrm{k}-7 \mathrm{~m})$ 
C)  $(11 \mathrm{k}+7 \mathrm{~m})^{2}$ 
D)  $(11 \mathrm{k}-7 \mathrm{~m})^{2}$

Question 7

Factor.
-$x^{2}-8 x-33$

Accepted Answer

A)  $(x+3)(x-11)$ 
B)  $(x-3)(x+1)$ 
C)  $(x-3)(x+11)$ 
D)  Prime 
A)  $(x+3)(x-11)$ 
B)  $(x-3)(x+1)$ 
C)  $(x-3)(x+11)$ 
D)  Prime

Question 8

Factor completely.
-$x^{2}+24 x+144$

Accepted Answer

A)  $(x+12)^{2}$ 
B)  Prime 
C)  $(\mathrm{x}+12)(\mathrm{x}-12)$ 
D)  $(\mathrm{x}-12)^{2}$ 
A)  $(x+12)^{2}$ 
B)  Prime 
C)  $(\mathrm{x}+12)(\mathrm{x}-12)$ 
D)  $(\mathrm{x}-12)^{2}$

Question 9

Provide an appropriate response.
-Why is the answer $\left(x^{2}-64\right)\left(x^{2}+64\right)$ not the correct answer to the instruction "Factor $\left(\mathrm{x}^{4}\right.$ - 4096) completely"?

Accepted Answer

The term @#LAT-DLM&

Question 10

Factor.
-$18 y^{2}+81 y-45$

Accepted Answer

A)  $9(2 y+1)(y-5)$ 
B)  $(2 y-1)(9 y+45)$ 
C)  $9(2 y-1)(y+5)$ 
D)  $(18 y-9)(y+5)$ 
A)  $9(2 y+1)(y-5)$ 
B)  $(2 y-1)(9 y+45)$ 
C)  $9(2 y-1)(y+5)$ 
D)  $(18 y-9)(y+5)$

Question 11

Factor completely.
-$5 x^{4}-5$

Accepted Answer

A)  $5\left(x^{2}+1\right)\left(x^{2}-1\right)$ 
B)  $5\left(x^{2}+1\right)(x+1)^{2}$ 
C)  $5\left(x^{2}+1\right)(x-1)^{2}$ 
D)  $5\left(x^{2}+1\right)(x+1)(x-1)$ 
A)  $5\left(x^{2}+1\right)\left(x^{2}-1\right)$ 
B)  $5\left(x^{2}+1\right)(x+1)^{2}$ 
C)  $5\left(x^{2}+1\right)(x-1)^{2}$ 
D)  $5\left(x^{2}+1\right)(x+1)(x-1)$

Question 12

Factor completely.
-$121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}$

Accepted Answer

A)  $(11 \mathrm{k}+7 \mathrm{~m})(11 \mathrm{k}-7 \mathrm{~m})$ 
B)  $(11 \mathrm{k}+7 \mathrm{~m})^{2}$ 
C)  $(11 \mathrm{k}-7 \mathrm{~m})^{2}$ 
D)  $(121 \mathrm{k}+\mathrm{m})(\mathrm{k}-49 \mathrm{~m})$ 
A)  $(11 \mathrm{k}+7 \mathrm{~m})(11 \mathrm{k}-7 \mathrm{~m})$ 
B)  $(11 \mathrm{k}+7 \mathrm{~m})^{2}$ 
C)  $(11 \mathrm{k}-7 \mathrm{~m})^{2}$ 
D)  $(121 \mathrm{k}+\mathrm{m})(\mathrm{k}-49 \mathrm{~m})$

Question 13

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

Accepted Answer

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

Question 14

Find the $x$-intercepts of the graph of the equation. (The grids are intentionally not included.)
-$y=2x^{2}-11x-6$

Accepted Answer

A)  $(6,0),\left(-\frac{5}{2}, 0\right)$ 
B)  $(6,0),\left(-\frac{1}{2}, 0\right)$ 
C)  $(6,0),(-1,0)$ 
D)  $(5,0),\left(-\frac{1}{2}, 0\right)$ 
A)  $(6,0),\left(-\frac{5}{2}, 0\right)$ 
B)  $(6,0),\left(-\frac{1}{2}, 0\right)$ 
C)  $(6,0),(-1,0)$ 
D)  $(5,0),\left(-\frac{1}{2}, 0\right)$

Question 15

Determine whether the following is a difference of squares.
-$121 x^{2}-4 y^{2}$

Accepted Answer

A) True 
 B)False

Question 16

Factor completely.
-$56 x^{2} y^{2}+15 x y-56$

Accepted Answer

A)  $(8 x y+7)(7 x y-8)$ 
B)  $(8 x y+7)(-7 x y+8)$ 
C)  $(8 x y-7)(7 x y-8)$ 
D)  $(8 x y-7)(7 x y+8)$ 
A)  $(8 x y+7)(7 x y-8)$ 
B)  $(8 x y+7)(-7 x y+8)$ 
C)  $(8 x y-7)(7 x y-8)$ 
D)  $(8 x y-7)(7 x y+8)$

Question 17

Solve the problem.
-Below is a diagram of a water slide. The slide is $21 \mathrm{ft}$ long. The ladder leading to the slide is $15 \mathrm{ft}$ long. How far is it from the end of the slide to the foot of the ladder? Round approximations to the nearest tenth.

Accepted Answer

A)  $18 \mathrm{ft}$ 
B)  $108 \mathrm{ft}$ 
C)  $7.4 \mathrm{ft}$ 
D)  $14.7 \mathrm{ft}$ 
A)  $18 \mathrm{ft}$ 
B)  $108 \mathrm{ft}$ 
C)  $7.4 \mathrm{ft}$ 
D)  $14.7 \mathrm{ft}$

Question 18

Factor using the ac-method.
-$21 x^{2}-91 x-70$

Accepted Answer

A)  $7(3 x+2)(x-5)$ 
B)  $7(3 x-2)(x+5)$ 
C)  prime 
D)  $(21 \mathrm{x}+14)(\mathrm{x}-5)$ 
A)  $7(3 x+2)(x-5)$ 
B)  $7(3 x-2)(x+5)$ 
C)  prime 
D)  $(21 \mathrm{x}+14)(\mathrm{x}-5)$

Question 19

Factor by grouping.
-$12 x^{4}-9 x^{2}-16 x^{2}+12$

Accepted Answer

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

Question 20

Solve the problem.
-The product of two consecutive odd integers is 195 . Find all pairs of integers that satisfy this condition.

Accepted Answer

A)  -15 and $-13,13$ and 15 
B)  - 15 and 13, - 13 and 15 
C)  -15 and 13 
D)  -15 and 15 
A)  -15 and $-13,13$ and 15 
B)  - 15 and 13, - 13 and 15 
C)  -15 and 13 
D)  -15 and 15

Solve using the principle of zero products. - $(x-0.4)(x+0.3)=0$

Factor. - $x^{2}-x-42$

Determine whether the following is a trinomial square. - $21 x^{2}-91 x-70$

Determine whether the following is a difference of squares. - $22 x^{2}-y^{2}$

Factor using the ac-method. - $10 x^{4}+23 x^{2}+12$

Factor completely. - $121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}$

Factor. - $x^{2}-8 x-33$

Factor completely. - $x^{2}+24 x+144$

Provide an appropriate response. -Why is the answer $\left(x^{2}-64\right)\left(x^{2}+64\right)$ not the correct answer to the instruction "Factor $\left(\mathrm{x}^{4}\right.$ - 4096) completely"?

Factor. - $18 y^{2}+81 y-45$

Factor completely. - $5 x^{4}-5$

Factor completely. - $121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}$

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

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=2x^{2}-11x-6$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2x^{2}-11x-6$

Determine whether the following is a difference of squares. - $121 x^{2}-4 y^{2}$

Factor completely. - $56 x^{2} y^{2}+15 x y-56$

Factor using the ac-method. - $21 x^{2}-91 x-70$

Factor by grouping. - $12 x^{4}-9 x^{2}-16 x^{2}+12$

Solve the problem. -The product of two consecutive odd integers is 195 . Find all pairs of integers that satisfy this condition.

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

Solve using the principle of zero products. - (x−0.4)(x+0.3)=0(x-0.4)(x+0.3)=0(x−0.4)(x+0.3)=0

Factor. - x2−x−42x^{2}-x-42x2−x−42

Determine whether the following is a trinomial square. - 21x2−91x−7021 x^{2}-91 x-7021x2−91x−70

Determine whether the following is a difference of squares. - 22x2−y222 x^{2}-y^{2}22x2−y2

Factor using the ac-method. - 10x4+23x2+1210 x^{4}+23 x^{2}+1210x4+23x2+12

Factor completely. - 121k2−49 m2121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}121k2−49 m2

Factor. - x2−8x−33x^{2}-8 x-33x2−8x−33

Factor completely. - x2+24x+144x^{2}+24 x+144x2+24x+144

Provide an appropriate response. -Why is the answer (x2−64)(x2+64)\left(x^{2}-64\right)\left(x^{2}+64\right)(x2−64)(x2+64) not the correct answer to the instruction "Factor (x4\left(\mathrm{x}^{4}\right.(x4 - 4096) completely"?

Factor. - 18y2+81y−4518 y^{2}+81 y-4518y2+81y−45

Factor completely. - 5x4−55 x^{4}-55x4−5

Factor completely. - 121k2−49 m2121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}121k2−49 m2

Factor completely. - 3x2+6x−xy−2y3 x^{2}+6 x-x y-2 y3x2+6x−xy−2y

Find the xxx -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2x2−11x−6y=2x^{2}-11x-6y=2x2−11x−6

Determine whether the following is a difference of squares. - 121x2−4y2121 x^{2}-4 y^{2}121x2−4y2

Factor completely. - 56x2y2+15xy−5656 x^{2} y^{2}+15 x y-5656x2y2+15xy−56

Solve the problem. -Below is a diagram of a water slide. The slide is 21ft21 \mathrm{ft}21ft long. The ladder leading to the slide is 15ft15 \mathrm{ft}15ft long. How far is it from the end of the slide to the foot of the ladder? Round approximations to the nearest tenth.

Factor using the ac-method. - 21x2−91x−7021 x^{2}-91 x-7021x2−91x−70

Factor by grouping. - 12x4−9x2−16x2+1212 x^{4}-9 x^{2}-16 x^{2}+1212x4−9x2−16x2+12

Solve the problem. -The product of two consecutive odd integers is 195 . Find all pairs of integers that satisfy this condition.

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

Solve using the principle of zero products. - $(x-0.4)(x+0.3)=0$

Factor. - $x^{2}-x-42$

Determine whether the following is a trinomial square. - $21 x^{2}-91 x-70$

Determine whether the following is a difference of squares. - $22 x^{2}-y^{2}$

Factor using the ac-method. - $10 x^{4}+23 x^{2}+12$

Factor completely. - $121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}$

Factor. - $x^{2}-8 x-33$

Factor completely. - $x^{2}+24 x+144$

Provide an appropriate response. -Why is the answer $\left(x^{2}-64\right)\left(x^{2}+64\right)$ not the correct answer to the instruction "Factor $\left(\mathrm{x}^{4}\right.$ - 4096) completely"?

Factor. - $18 y^{2}+81 y-45$

Factor completely. - $5 x^{4}-5$

Factor completely. - $121 \mathrm{k}^{2}-49 \mathrm{~m}^{2}$

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

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) - $y=2x^{2}-11x-6$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) - y=2x^{2}-11x-6$

Determine whether the following is a difference of squares. - $121 x^{2}-4 y^{2}$

Factor completely. - $56 x^{2} y^{2}+15 x y-56$

Factor using the ac-method. - $21 x^{2}-91 x-70$

Factor by grouping. - $12 x^{4}-9 x^{2}-16 x^{2}+12$