Question 1

Solve.
-Use the following graph to solve $x^{2}+3 x-4=0$.
$$y=x^{2}+3 x-4$$

Accepted Answer

A)  4,1 
B)  $-4,1$ 
C)  $-1,4$ 
D)  $-4,-1$ 
A)  4,1 
B)  $-4,1$ 
C)  $-1,4$ 
D)  $-4,-1$

Question 2

Factor.
-$4 x^{6}-40 x^{5}-96 x^{4}$

Accepted Answer

A)  $4 x^{4}(x-6)(x-4)$ 
B)  $4 x^{4}\left(x^{2}-4 x-24\right)$ 
C)  $4 x^{4}(x-6)(x+4)$ 
D)  $4 x^{3}\left(x^{2}-4 x-24\right)$ 
A)  $4 x^{4}(x-6)(x-4)$ 
B)  $4 x^{4}\left(x^{2}-4 x-24\right)$ 
C)  $4 x^{4}(x-6)(x+4)$ 
D)  $4 x^{3}\left(x^{2}-4 x-24\right)$

Question 3

Factor.
-$15 x^{2}+22 x+8$

Accepted Answer

A)  Prime 
B)  $(3 x+2)(5 x+4)$ 
C)  $(3 \mathrm{x}-2)(5 \mathrm{x}-4)$ 
D)  $(15 x+2)(x+4)$ 
A)  Prime 
B)  $(3 x+2)(5 x+4)$ 
C)  $(3 \mathrm{x}-2)(5 \mathrm{x}-4)$ 
D)  $(15 x+2)(x+4)$

Question 4

Factor.
-$2 m(7-m)+3 n(7-m)$

Accepted Answer

A)  $m(2+3 n)(7-1)$ 
B)  $(2 m-3 n)(7-m)$ 
C)  No common factor 
D)  $(2 m+3 n)(7-m)$ 
A)  $m(2+3 n)(7-1)$ 
B)  $(2 m-3 n)(7-m)$ 
C)  No common factor 
D)  $(2 m+3 n)(7-m)$

Question 5

Factor.
-$5 x^{3}+15 x^{2}-50 x$

Accepted Answer

A)  $5 x(x-2)(x+5)$ 
B)  $\left(5 x^{2}+10 x\right)(x-5)$ 
C)  $5 x(x+2)(x-5)$ 
D)  $(x-2)\left(5 x^{2}+25\right)$ 
A)  $5 x(x-2)(x+5)$ 
B)  $\left(5 x^{2}+10 x\right)(x-5)$ 
C)  $5 x(x+2)(x-5)$ 
D)  $(x-2)\left(5 x^{2}+25\right)$

Question 6

Factor.
-$y^{2}-\frac{2}{7} y+\frac{1}{49}$

Accepted Answer

A)  y $\left(y-\frac{2}{7}\right)$ 
B)  Prime 
C)  $\left(y+\frac{1}{7}\right)^{2}$ 
D)  $\left(y-\frac{1}{7}\right)^{2}$ 
A)  y $\left(y-\frac{2}{7}\right)$ 
B)  Prime 
C)  $\left(y+\frac{1}{7}\right)^{2}$ 
D)  $\left(y-\frac{1}{7}\right)^{2}$

Question 7

Factor.
-$96 x^{2}+56 x y+8 y^{2}$

Accepted Answer

A)  $(24 \mathrm{x}+8 \mathrm{y})(4 \mathrm{x}+\mathrm{y})$ 
B)  $8(3 x-y)(4 x-y)$ 
C)  $(3 x+y)(8 x+3 y)$ 
D)  $8(3 x+y)(4 x+y)$ 
A)  $(24 \mathrm{x}+8 \mathrm{y})(4 \mathrm{x}+\mathrm{y})$ 
B)  $8(3 x-y)(4 x-y)$ 
C)  $(3 x+y)(8 x+3 y)$ 
D)  $8(3 x+y)(4 x+y)$

Question 8

Factor completely.
-$196 \mathrm{x}^{2}-36$

Accepted Answer

A)  $4(7 x-3)(7 x+3)$ 
B)  $(7 x-3)(28 x+12)$ 
C)  $4(7 x+3)^{2}$ 
D)  $(28 \mathrm{x}-12)(7 \mathrm{x}+3)$ 
A)  $4(7 x-3)(7 x+3)$ 
B)  $(7 x-3)(28 x+12)$ 
C)  $4(7 x+3)^{2}$ 
D)  $(28 \mathrm{x}-12)(7 \mathrm{x}+3)$

Question 9

Factor.
-$8 x^{3}+18 x^{2}+9 x$

Accepted Answer

A)  $x(4 x+3)(2 x+3)$ 
B)  $x(8 x+1)(x+9)$ 
C)  $x(4 x-3)(2 x-3)$ 
D)  $\left(8 x^{2}+3\right)(x+3)$ 
A)  $x(4 x+3)(2 x+3)$ 
B)  $x(8 x+1)(x+9)$ 
C)  $x(4 x-3)(2 x-3)$ 
D)  $\left(8 x^{2}+3\right)(x+3)$

Question 10

Factor.
-$u^{2}-4 u v-12 v^{2}$

Accepted Answer

A)  $(u-2 v)(u+6 v)$ 
B)  $(u-v)(u+6 v)$ 
C)  $(u+2 v)(u-6 v)$ 
D)  $(u-2 v)(u+v)$ 
A)  $(u-2 v)(u+6 v)$ 
B)  $(u-v)(u+6 v)$ 
C)  $(u+2 v)(u-6 v)$ 
D)  $(u-2 v)(u+v)$

Question 11

Factor.
-$36 m^{7}+42 m^{4}+12 m^{2}$

Accepted Answer

A)  $6 m^{2}\left(6 m^{5}+7 m^{2}+2\right)$ 
B)  No common factor 
C)  $6\left(6 m^{7}+7 m^{4}+2 m^{2}\right)$ 
D)  $m^{2}\left(36 m^{5}+42 m^{2}+12\right)$ 
A)  $6 m^{2}\left(6 m^{5}+7 m^{2}+2\right)$ 
B)  No common factor 
C)  $6\left(6 m^{7}+7 m^{4}+2 m^{2}\right)$ 
D)  $m^{2}\left(36 m^{5}+42 m^{2}+12\right)$

Question 12

Solve.
-Use the following graph to solve $-x^{2}-5 x+6=0$.
 
$$y=-x^{2}-5 x+6$$

Accepted Answer

A)  -6 
B)  6 
C)  $1,-6$ 
D)  $-1,6$ 
A)  -6 
B)  6 
C)  $1,-6$ 
D)  $-1,6$

Question 13

Factor by grouping.
-$x^{3}+8 x^{2}+7 x+56$

Accepted Answer

A)  $(x+8 x)\left(x^{2}+7\right)$ 
B)  $(\mathrm{x}-8)\left(\mathrm{x}^{3}+7\right)$ 
C)  $(x+8)\left(x^{2}+7\right)$ 
D)  $(x+8)\left(x^{2}-7\right)$ 
A)  $(x+8 x)\left(x^{2}+7\right)$ 
B)  $(\mathrm{x}-8)\left(\mathrm{x}^{3}+7\right)$ 
C)  $(x+8)\left(x^{2}+7\right)$ 
D)  $(x+8)\left(x^{2}-7\right)$

Question 14

Factor.
-$\mathrm{p}^{4}-15 \mathrm{p}^{2}+56$

Accepted Answer

A)  $\left(p^{2}-7\right)\left(p^{2}+8\right)$ 
B)  $\left(p^{2}-7\right)\left(p^{2}-8\right)$ 
C)  $\left(p^{2}-56\right)\left(p^{2}-1\right)$ 
D)  $p^{2}(p-7)(p-8)$ 
A)  $\left(p^{2}-7\right)\left(p^{2}+8\right)$ 
B)  $\left(p^{2}-7\right)\left(p^{2}-8\right)$ 
C)  $\left(p^{2}-56\right)\left(p^{2}-1\right)$ 
D)  $p^{2}(p-7)(p-8)$

Question 15

Factor completely.
-$a^{2}-30 a b+225 b^{2}$

Accepted Answer

A)  $(a+15 b)^{2}$ 
B)  Prime 
C)  $(a+15 b)(a-15 b)$ 
D)  $(a-15 b)^{2}$ 
A)  $(a+15 b)^{2}$ 
B)  Prime 
C)  $(a+15 b)(a-15 b)$ 
D)  $(a-15 b)^{2}$

Question 16

Factor.
-$x^{2}+\frac{2}{11} x+\frac{1}{121}$

Accepted Answer

A)  Prime 
B)  $x\left(x+\frac{2}{11}\right)$ 
C)  $\left(x+\frac{1}{11}\right)^{2}$ 
D)  $\left(x+\frac{2}{11}\right)^{2}$ 
A)  Prime 
B)  $x\left(x+\frac{2}{11}\right)$ 
C)  $\left(x+\frac{1}{11}\right)^{2}$ 
D)  $\left(x+\frac{2}{11}\right)^{2}$

Question 17

Factor completely.
-$x^{2}-14 x y+49 y^{2}$

Accepted Answer

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

Question 18

Solve by factoring and using the principle of zero products.
-$x^{2}-x=20$

Accepted Answer

A)  $-4,-5$ 
B)  1,20 
C)  $-4,5$ 
D)  4,5 
A)  $-4,-5$ 
B)  1,20 
C)  $-4,5$ 
D)  4,5

Question 19

Factor using the ac-method.
-$6 x^{2}+17 x+12$

Accepted Answer

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

Question 20

Solve the problem.
-A number is 30 less than its square. Find all such numbers.

Accepted Answer

A)  -6 and 6 
B)  -5 and 5 
C)  -6 and 5 
D)  -5 and 6 
A)  -6 and 6 
B)  -5 and 5 
C)  -6 and 5 
D)  -5 and 6

Solve. -Use the following graph to solve $x^{2}+3 x-4=0$ . $y=x^{2}+3 x-4$ $Solve. -Use the following graph to solve x^{2}+3 x-4=0 . y=x^{2}+3 x-4$

Factor. - $4 x^{6}-40 x^{5}-96 x^{4}$

Factor. - $15 x^{2}+22 x+8$

Factor. - $2 m(7-m)+3 n(7-m)$

Factor. - $5 x^{3}+15 x^{2}-50 x$

Factor. - $y^{2}-\frac{2}{7} y+\frac{1}{49}$

Factor. - $96 x^{2}+56 x y+8 y^{2}$

Factor completely. - $196 \mathrm{x}^{2}-36$

Factor. - $8 x^{3}+18 x^{2}+9 x$

Factor. - $u^{2}-4 u v-12 v^{2}$

Factor. - $36 m^{7}+42 m^{4}+12 m^{2}$

Solve. -Use the following graph to solve $-x^{2}-5 x+6=0$ . $Solve. -Use the following graph to solve -x^{2}-5 x+6=0 . y=-x^{2}-5 x+6$ $y=-x^{2}-5 x+6$

Factor by grouping. - $x^{3}+8 x^{2}+7 x+56$

Factor. - $\mathrm{p}^{4}-15 \mathrm{p}^{2}+56$

Factor completely. - $a^{2}-30 a b+225 b^{2}$

Factor. - $x^{2}+\frac{2}{11} x+\frac{1}{121}$

Factor completely. - $x^{2}-14 x y+49 y^{2}$

Solve by factoring and using the principle of zero products. - $x^{2}-x=20$

Factor using the ac-method. - $6 x^{2}+17 x+12$

Solve the problem. -A number is 30 less than its square. Find all such numbers.

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+3x−4=0x^{2}+3 x-4=0x2+3x−4=0 . y=x2+3x−4y=x^{2}+3 x-4y=x2+3x−4

Factor. - 4x6−40x5−96x44 x^{6}-40 x^{5}-96 x^{4}4x6−40x5−96x4

Factor. - 15x2+22x+815 x^{2}+22 x+815x2+22x+8

Factor. - 2m(7−m)+3n(7−m)2 m(7-m)+3 n(7-m)2m(7−m)+3n(7−m)

Factor. - 5x3+15x2−50x5 x^{3}+15 x^{2}-50 x5x3+15x2−50x

Factor. - y2−27y+149y^{2}-\frac{2}{7} y+\frac{1}{49}y2−72​y+491​

Factor. - 96x2+56xy+8y296 x^{2}+56 x y+8 y^{2}96x2+56xy+8y2

Factor completely. - 196x2−36196 \mathrm{x}^{2}-36196x2−36

Factor. - 8x3+18x2+9x8 x^{3}+18 x^{2}+9 x8x3+18x2+9x

Factor. - u2−4uv−12v2u^{2}-4 u v-12 v^{2}u2−4uv−12v2

Factor. - 36m7+42m4+12m236 m^{7}+42 m^{4}+12 m^{2}36m7+42m4+12m2

Solve. -Use the following graph to solve −x2−5x+6=0-x^{2}-5 x+6=0−x2−5x+6=0 . y=−x2−5x+6y=-x^{2}-5 x+6y=−x2−5x+6

Factor by grouping. - x3+8x2+7x+56x^{3}+8 x^{2}+7 x+56x3+8x2+7x+56

Factor. - p4−15p2+56\mathrm{p}^{4}-15 \mathrm{p}^{2}+56p4−15p2+56

Factor completely. - a2−30ab+225b2a^{2}-30 a b+225 b^{2}a2−30ab+225b2

Factor. - x2+211x+1121x^{2}+\frac{2}{11} x+\frac{1}{121}x2+112​x+1211​

Factor completely. - x2−14xy+49y2x^{2}-14 x y+49 y^{2}x2−14xy+49y2

Solve by factoring and using the principle of zero products. - x2−x=20x^{2}-x=20x2−x=20

Factor using the ac-method. - 6x2+17x+126 x^{2}+17 x+126x2+17x+12