Question 1

Solve.
-Use the following graph to solve $x^{2}-4 x-5=0$.
$$y=x^{2}-4 x-5$$

Accepted Answer

A)  $-5,-1$ 
B)  $-5,1$ 
C)  1,5 
D)  $-1,5$ 
A)  $-5,-1$ 
B)  $-5,1$ 
C)  1,5 
D)  $-1,5$

Question 2

Provide an appropriate response.
-Use the FOIL method to show that $(3 x+6)(x-5)$ is $3 x^{2}-9 x-30$. If you were asked to completely factor $3 x^{2}-9 x-30$, why would it be incorrect to give $(3 x+6)(x-5)$ as your answer?

Accepted Answer

The factor

Question 3

Factor.
-$24-5 x-x^{2}$

Accepted Answer

A)  $(x+8)(x-3)$ 
B)  $(-x-8)(x-3)$ 
C)  $(x-8)(x-3)$ 
D)  $(-x-3)(x-8)$ 
A)  $(x+8)(x-3)$ 
B)  $(-x-8)(x-3)$ 
C)  $(x-8)(x-3)$ 
D)  $(-x-3)(x-8)$

Question 4

Factor completely.
-$u^{2}-7 u v-18 v^{2}$

Accepted Answer

A)  $(u-2 v)(u+v)$ 
B)  $(u-v)(u+9 v)$ 
C)  $(u-2 v)(u+9 v)$ 
D)  $(u+2 v)(u-9 v)$ 
A)  $(u-2 v)(u+v)$ 
B)  $(u-v)(u+9 v)$ 
C)  $(u-2 v)(u+9 v)$ 
D)  $(u+2 v)(u-9 v)$

Question 5

Solve the problem.
-A rectangular garden is three times as long as it is wide. If the area of the garden is $588 \mathrm{ft}^{2}$, find the length and width of the garden.

Accepted Answer

A)  length: $196 \mathrm{ft}$; width: $3 \mathrm{ft}$ 
B)  length: $39 \mathrm{ft}$; width: $13 \mathrm{ft}$ 
C)  length: $42 \mathrm{ft}$; width: $14 \mathrm{ft}$ 
D)  length: $14 \mathrm{ft}$; width: $\frac{14}{3} \mathrm{ft}$ 
A)  length: $196 \mathrm{ft}$; width: $3 \mathrm{ft}$ 
B)  length: $39 \mathrm{ft}$; width: $13 \mathrm{ft}$ 
C)  length: $42 \mathrm{ft}$; width: $14 \mathrm{ft}$ 
D)  length: $14 \mathrm{ft}$; width: $\frac{14}{3} \mathrm{ft}$

Question 6

Factor completely.
-$3 \mathrm{x}^{8}-768$

Accepted Answer

A)  $3\left(x^{4}+16\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
B)  $3\left(x^{4}-16\right)^{2}$ 
C)  $3\left(x^{4}+16\right)\left(x^{4}-16\right)$ 
D)  $\left(3 x^{4}+48\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
A)  $3\left(x^{4}+16\right)\left(x^{2}+4\right)(x+2)(x-2)$ 
B)  $3\left(x^{4}-16\right)^{2}$ 
C)  $3\left(x^{4}+16\right)\left(x^{4}-16\right)$ 
D)  $\left(3 x^{4}+48\right)\left(x^{2}+4\right)(x+2)(x-2)$

Question 7

Solve by factoring and using the principle of zero products.
-$81 \mathrm{k}^{2}=16$

Accepted Answer

A)  $\frac{9}{4}, 0$ 
B)  4,0 
C)  $\frac{4}{9},-\frac{4}{9}$ 
D)  $\frac{9}{4},-\frac{9}{4}$ 
A)  $\frac{9}{4}, 0$ 
B)  4,0 
C)  $\frac{4}{9},-\frac{4}{9}$ 
D)  $\frac{9}{4},-\frac{9}{4}$

Question 8

Factor completely.
-$y^{2}-49$

Accepted Answer

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

Question 9

Factor completely.
-$16+8 x+x^{2}$

Accepted Answer

A)  $(x-4)^{2}$ 
B)  $(x+4)^{2}$ 
C)  $(x+4)(x-4)$ 
D)  Prime 
A)  $(x-4)^{2}$ 
B)  $(x+4)^{2}$ 
C)  $(x+4)(x-4)$ 
D)  Prime

Question 10

Factor.
-$t^{2}+0.4 t-0.12$

Accepted Answer

A)  $(t-0.6)(t+0.2)$ 
B)  $(t+0.6)(t-0.2)$ 
C)  $(t+0.12)(t-1)$ 
D)  $(t+0.2)^{2}$ 
A)  $(t-0.6)(t+0.2)$ 
B)  $(t+0.6)(t-0.2)$ 
C)  $(t+0.12)(t-1)$ 
D)  $(t+0.2)^{2}$

Question 11

Factor by grouping.
-$s^{2}+6 s+7 s+42$

Accepted Answer

A)  $(s-6)(s-7)$ 
B)  $(s+6)(s-7)$ 
C)  $(s+6)(s+7)$ 
D)  $\mathrm{s}(\mathrm{s}+55)$ 
A)  $(s-6)(s-7)$ 
B)  $(s+6)(s-7)$ 
C)  $(s+6)(s+7)$ 
D)  $\mathrm{s}(\mathrm{s}+55)$

Question 12

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

Accepted Answer

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

Question 13

Determine whether the following is a difference of squares.
-$x^{2}+64$

Accepted Answer

A) True 
 B)False

Question 14

Factor by grouping.
-$8 x^{2}-20 x y+10 x y-25 y^{2}$

Accepted Answer

A)  $(8 x+5 y)(x-5 y)$ 
B)  $(4 \mathrm{x}+5)(2 \mathrm{x}-5)$ 
C)  $(4 x+5 y)(2 x-5 y)$ 
D)  $(4 x-5 y)(2 x-5 y)$ 
A)  $(8 x+5 y)(x-5 y)$ 
B)  $(4 \mathrm{x}+5)(2 \mathrm{x}-5)$ 
C)  $(4 x+5 y)(2 x-5 y)$ 
D)  $(4 x-5 y)(2 x-5 y)$

Question 15

Factor completely.
-$x^{3}+2 x^{2}-25 x-50$

Accepted Answer

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

Question 16

Factor.
-$y^{2}+0.3 y-0.4$

Accepted Answer

A)  $(y-0.8)(y+0.5)$ 
B)  $(y+0.8)(y-0.5)$ 
C)  $(\mathrm{y}-0.8)(\mathrm{y}-0.5)$ 
D)  $(y+0.15)^{2}$ 
A)  $(y-0.8)(y+0.5)$ 
B)  $(y+0.8)(y-0.5)$ 
C)  $(\mathrm{y}-0.8)(\mathrm{y}-0.5)$ 
D)  $(y+0.15)^{2}$

Question 17

Factor.
-$t^{2}+1.1 t+0.3$

Accepted Answer

A)  Prime 
B)  $(t+1.1)(t+0.3)$ 
C)  $(t+0.6)(t+0.5)$ 
D)  $(t+0.55)^{2}$ 
A)  Prime 
B)  $(t+1.1)(t+0.3)$ 
C)  $(t+0.6)(t+0.5)$ 
D)  $(t+0.55)^{2}$

Question 18

Determine whether the following is a trinomial square.
-$x^{2}-16 x-64$

Accepted Answer

A) True 
 B)False

Question 19

Factor.
-$3 x^{2}-15 x+18$

Accepted Answer

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

Question 20

Factor.
-$18 x^{3}-78 x^{2}-60 x$

Accepted Answer

A)  $\left(x^{2}-5\right)(18 x+12)$ 
B)  $x(3 x+2)(6 x-30)$ 
C)  $6(3 x-2)(x+5)$ 
D)  $6 x(3 x+2)(x-5)$ 
A)  $\left(x^{2}-5\right)(18 x+12)$ 
B)  $x(3 x+2)(6 x-30)$ 
C)  $6(3 x-2)(x+5)$ 
D)  $6 x(3 x+2)(x-5)$

Solve. -Use the following graph to solve $x^{2}-4 x-5=0$ . $y=x^{2}-4 x-5$ $Solve. -Use the following graph to solve x^{2}-4 x-5=0 . y=x^{2}-4 x-5$

Provide an appropriate response. -Use the FOIL method to show that $(3 x+6)(x-5)$ is $3 x^{2}-9 x-30$ . If you were asked to completely factor $3 x^{2}-9 x-30$ , why would it be incorrect to give $(3 x+6)(x-5)$ as your answer?

Factor. - $24-5 x-x^{2}$

Factor completely. - $u^{2}-7 u v-18 v^{2}$

Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is $588 \mathrm{ft}^{2}$ , find the length and width of the garden.

Factor completely. - $3 \mathrm{x}^{8}-768$

Solve by factoring and using the principle of zero products. - $81 \mathrm{k}^{2}=16$

Factor completely. - $y^{2}-49$

Factor completely. - $16+8 x+x^{2}$

Factor. - $t^{2}+0.4 t-0.12$

Factor by grouping. - $s^{2}+6 s+7 s+42$

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

Determine whether the following is a difference of squares. - $x^{2}+64$

Factor by grouping. - $8 x^{2}-20 x y+10 x y-25 y^{2}$

Factor completely. - $x^{3}+2 x^{2}-25 x-50$

Factor. - $y^{2}+0.3 y-0.4$

Factor. - $t^{2}+1.1 t+0.3$

Determine whether the following is a trinomial square. - $x^{2}-16 x-64$

Factor. - $3 x^{2}-15 x+18$

Factor. - $18 x^{3}-78 x^{2}-60 x$

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. -Use the following graph to solve x2−4x−5=0x^{2}-4 x-5=0x2−4x−5=0 . y=x2−4x−5y=x^{2}-4 x-5y=x2−4x−5

Factor. - 24−5x−x224-5 x-x^{2}24−5x−x2

Factor completely. - u2−7uv−18v2u^{2}-7 u v-18 v^{2}u2−7uv−18v2

Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is 588ft2588 \mathrm{ft}^{2}588ft2 , find the length and width of the garden.

Factor completely. - 3x8−7683 \mathrm{x}^{8}-7683x8−768

Solve by factoring and using the principle of zero products. - 81k2=1681 \mathrm{k}^{2}=1681k2=16

Factor completely. - y2−49y^{2}-49y2−49

Factor completely. - 16+8x+x216+8 x+x^{2}16+8x+x2

Factor. - t2+0.4t−0.12t^{2}+0.4 t-0.12t2+0.4t−0.12

Factor by grouping. - s2+6s+7s+42s^{2}+6 s+7 s+42s2+6s+7s+42

Factor. - 4x2−12xt+9t24 x^{2}-12 x t+9 t^{2}4x2−12xt+9t2

Determine whether the following is a difference of squares. - x2+64x^{2}+64x2+64

Factor by grouping. - 8x2−20xy+10xy−25y28 x^{2}-20 x y+10 x y-25 y^{2}8x2−20xy+10xy−25y2

Factor completely. - x3+2x2−25x−50x^{3}+2 x^{2}-25 x-50x3+2x2−25x−50

Factor. - y2+0.3y−0.4y^{2}+0.3 y-0.4y2+0.3y−0.4

Factor. - t2+1.1t+0.3t^{2}+1.1 t+0.3t2+1.1t+0.3

Determine whether the following is a trinomial square. - x2−16x−64x^{2}-16 x-64x2−16x−64

Factor. - 3x2−15x+183 x^{2}-15 x+183x2−15x+18

Factor. - 18x3−78x2−60x18 x^{3}-78 x^{2}-60 x18x3−78x2−60x