Question 1

Factor by grouping.
-$b x+x+b+1$

Accepted Answer

A)  $(b x+1)(x+b)$ 
B)  $(b+1)(x+1)$ 
C)  $(b+1)(x+b)$ 
D)  $(b x+b)(x+1)$ 
A)  $(b x+1)(x+b)$ 
B)  $(b+1)(x+1)$ 
C)  $(b+1)(x+b)$ 
D)  $(b x+b)(x+1)$ B

Question 2

Find all solutions by factoring.
-$2 k^{2}=-9 \mathrm{k}-9$

Accepted Answer

A)  $\left\{3,-\frac{3}{2}\right\}$ 
B)  $\left\{3, \frac{3}{2}\right\}$ 
C)  $\left\{-\frac{3}{2},-3\right\}$ 
D)  $\{-3,-6\}$ 
A)  $\left\{3,-\frac{3}{2}\right\}$ 
B)  $\left\{3, \frac{3}{2}\right\}$ 
C)  $\left\{-\frac{3}{2},-3\right\}$ 
D)  $\{-3,-6\}$ C

Question 3

Factor the polynomial completely
-$9 x^{2}-24 x+16-y^{2}$

Accepted Answer

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

Question 4

Factor the polynomial completely
-$36-(m+2 n)^{2}$

Accepted Answer

A)  $(6+m+2 n)(6-m+2 n)$ 
B)  $(6+m+2 n)(6-m-2 n)$ 
C)  $(6-m-2 n)(-6-m-2 n)$ 
D)  $(36+m+2 n)(36-m-2 n)$ 
A)  $(6+m+2 n)(6-m+2 n)$ 
B)  $(6+m+2 n)(6-m-2 n)$ 
C)  $(6-m-2 n)(-6-m-2 n)$ 
D)  $(36+m+2 n)(36-m-2 n)$

Question 5

Factor the polynomial completely
-$t^{3}+216$

Accepted Answer

A)  $(t+6)\left(t^{2}+36\right)$ 
B)  $(t+6)\left(t^{2}-6 t+36\right)$ 
C)  $(t-216)\left(t^{2}-1\right)$ 
D)  $(t-6)\left(t^{2}+6 t+36\right)$ 
A)  $(t+6)\left(t^{2}+36\right)$ 
B)  $(t+6)\left(t^{2}-6 t+36\right)$ 
C)  $(t-216)\left(t^{2}-1\right)$ 
D)  $(t-6)\left(t^{2}+6 t+36\right)$

Question 6

Solve the equation.
-$(8 y+7)(5 y+11)=0$

Accepted Answer

A)  $\left\{-\frac{7}{8},-\frac{11}{5}\right\}$ 
B)  $\left\{-\frac{8}{-1},-\frac{5}{11}\right\}$ 
C)  $\{-1,6\}$ 
D)  $\left\{\frac{7}{8}, \frac{11}{5}\right\}$ 
A)  $\left\{-\frac{7}{8},-\frac{11}{5}\right\}$ 
B)  $\left\{-\frac{8}{-1},-\frac{5}{11}\right\}$ 
C)  $\{-1,6\}$ 
D)  $\left\{\frac{7}{8}, \frac{11}{5}\right\}$

Question 7

Factor the trinomial completely.
-$-36 x^{2}-30 x+36$

Accepted Answer

A)  $(-18 x+12)(2 x+3)$ 
B)  $6(3 x+2)(-2 x+3)$ 
C)  $(-3 x+2)(12 x+18)$ 
D)  $-6(3 x-2)(2 x+3)$ 
A)  $(-18 x+12)(2 x+3)$ 
B)  $6(3 x+2)(-2 x+3)$ 
C)  $(-3 x+2)(12 x+18)$ 
D)  $-6(3 x-2)(2 x+3)$

Question 8

Factor the trinomial completely.
-$x^{2}+4 x y-21 y^{2}$

Accepted Answer

A)  $(x-7 y)(x+3 y)$ 
B)  $(x-y)(x+3 y)$ 
C)  $(x-7 y)(x+y)$ 
D)  $(x+7 y)(x-3 y)$ 
A)  $(x-7 y)(x+3 y)$ 
B)  $(x-y)(x+3 y)$ 
C)  $(x-7 y)(x+y)$ 
D)  $(x+7 y)(x-3 y)$

Question 9

Factor the polynomial completely
-$81 \mathrm{k}^{3} \mathrm{~m}-375 \mathrm{~m}^{4}$

Accepted Answer

A)  $3 \mathrm{~m}\left(3 \mathrm{k}+5 \mathrm{~m}^{2}\right)\left(9 \mathrm{k}^{2}-15 \mathrm{~km}+25 \mathrm{~km}^{2}\right)$ 
B)  $3 m(3 k-5 m)\left(9 k^{2}+15 k m+25 m^{2}\right)$ 
C)  $\left(9 \mathrm{~km}-15 \mathrm{~m}^{2}\right)\left(9 \mathrm{k}^{2}+25 \mathrm{~m}^{2}\right)$ 
D)  $3 \mathrm{~m}(27 \mathrm{k}-5 \mathrm{~m})\left(\mathrm{k}^{2}+15 \mathrm{~km}+25 \mathrm{~m}^{2}\right)$ 
A)  $3 \mathrm{~m}\left(3 \mathrm{k}+5 \mathrm{~m}^{2}\right)\left(9 \mathrm{k}^{2}-15 \mathrm{~km}+25 \mathrm{~km}^{2}\right)$ 
B)  $3 m(3 k-5 m)\left(9 k^{2}+15 k m+25 m^{2}\right)$ 
C)  $\left(9 \mathrm{~km}-15 \mathrm{~m}^{2}\right)\left(9 \mathrm{k}^{2}+25 \mathrm{~m}^{2}\right)$ 
D)  $3 \mathrm{~m}(27 \mathrm{k}-5 \mathrm{~m})\left(\mathrm{k}^{2}+15 \mathrm{~km}+25 \mathrm{~m}^{2}\right)$

Question 10

Factor the polynomial completely
-$125 a^{3}-64 b^{3}$

Accepted Answer

A)  $\left(5 a+4 b^{2}\right)\left(25 a^{2}-20 a b+16 b^{2}\right)$ 
B)  $(5 a-4 b)\left(25 a^{2}+16 b^{2}\right)$ 
C)  $(5 a-4 b)\left(25 a^{2}+20 a b+16 b^{2}\right)$ 
D)  $(125 a-4 b)\left(a^{2}+20 a b+16 b^{2}\right)$ 
A)  $\left(5 a+4 b^{2}\right)\left(25 a^{2}-20 a b+16 b^{2}\right)$ 
B)  $(5 a-4 b)\left(25 a^{2}+16 b^{2}\right)$ 
C)  $(5 a-4 b)\left(25 a^{2}+20 a b+16 b^{2}\right)$ 
D)  $(125 a-4 b)\left(a^{2}+20 a b+16 b^{2}\right)$

Question 11

Explain why a cubic equation of the form $\mathrm{ax}^{3}+\mathrm{bx} \mathrm{x}^{2}+\mathrm{cx}=0$ must have 0 in its solution set.

Accepted Answer

Explanations will vary. One possibility:

Question 12

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

Accepted Answer

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

Question 13

actor out the greatest common factor. Simplify the factors, if possible
-$3(2-x)^{2}-(2-x)^{3}+4(2-x)$

Accepted Answer

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

Question 14

Factor the polynomial completely
-$49 x^{6}+84 x^{3}+36$

Accepted Answer

A)  $49 x^{6}+84 x^{3}+84$ 
B)  $\left(7 x^{3}+6\right)^{2}$ 
C)  $\left(7 x^{3}-6\right)^{2}$ 
D)  $\left(7 x^{3}-6\right)\left(7 x^{3}+6\right)$ 
A)  $49 x^{6}+84 x^{3}+84$ 
B)  $\left(7 x^{3}+6\right)^{2}$ 
C)  $\left(7 x^{3}-6\right)^{2}$ 
D)  $\left(7 x^{3}-6\right)\left(7 x^{3}+6\right)$

Question 15

$5 p^{2}+4 p q-q^{2}$

Accepted Answer

A)  $(5 p+q)(p-q)$ 
B)  cannot be factored 
C)  $(5 p-1)\left(p+q^{2}\right)$ 
D)  $(5 p-q)(p+q)$ 
A)  $(5 p+q)(p-q)$ 
B)  cannot be factored 
C)  $(5 p-1)\left(p+q^{2}\right)$ 
D)  $(5 p-q)(p+q)$

Question 16

Factor the polynomial completely
-$147 a^{4}-48 b^{2}$

Accepted Answer

A)  $3\left(7 a^{2}+4 b\right)\left(7 a^{2}-4 b\right)$ 
B)  $3\left(7 a^{2}-4 b\right)^{2}$ 
C)  $\left(21 a^{2}+12 b\right)\left(7 a^{2}-4 b\right)$ 
D)  $3\left(7 a^{2}+4 b\right)^{2}$ 
A)  $3\left(7 a^{2}+4 b\right)\left(7 a^{2}-4 b\right)$ 
B)  $3\left(7 a^{2}-4 b\right)^{2}$ 
C)  $\left(21 a^{2}+12 b\right)\left(7 a^{2}-4 b\right)$ 
D)  $3\left(7 a^{2}+4 b\right)^{2}$

Question 17

Which one of the following is not a factored form of $-x^{2}+1 x+56$ ?

Accepted Answer

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

Question 18

Solve the equation
-$9 t^{3}-49 t=0$

Accepted Answer

A)  $\left\{ \pm \frac{7}{3}\right\}$ 
B)  $\left\{\frac{7}{3}\right\}$ 
C)  $\left\{\frac{-7}{3}, \frac{7}{3}, 0\right\}$ 
D)  $\{0\}$ 
A)  $\left\{ \pm \frac{7}{3}\right\}$ 
B)  $\left\{\frac{7}{3}\right\}$ 
C)  $\left\{\frac{-7}{3}, \frac{7}{3}, 0\right\}$ 
D)  $\{0\}$

Question 19

Factor the polynomial
-$9 x^{2}+48 x y+64 y^{2}$

Accepted Answer

A)  $(9 x+1)(x+64)$ 
B)  $(3 x+8 y)^{2}$ 
C)  $(3 x+8 y)(3 x-8 y)$ 
D)  $(3 x-8 y)^{2}$ 
A)  $(9 x+1)(x+64)$ 
B)  $(3 x+8 y)^{2}$ 
C)  $(3 x+8 y)(3 x-8 y)$ 
D)  $(3 x-8 y)^{2}$

Question 20

Factor by grouping.
-$8 y x+9 x+48 y+54$

Accepted Answer

A)  $(8 y+6)(x+9)$ 
B)  $(8 y+1)(x+54)$ 
C)  $(y+9)(8 x+6)$ 
D)  $(8 y+9)(x+6)$ 
A)  $(8 y+6)(x+9)$ 
B)  $(8 y+1)(x+54)$ 
C)  $(y+9)(8 x+6)$ 
D)  $(8 y+9)(x+6)$

Factor by grouping. - $b x+x+b+1$

Find all solutions by factoring. - $2 k^{2}=-9 \mathrm{k}-9$

Factor the polynomial completely - $9 x^{2}-24 x+16-y^{2}$

Factor the polynomial completely - $36-(m+2 n)^{2}$

Factor the polynomial completely - $t^{3}+216$

Solve the equation. - $(8 y+7)(5 y+11)=0$

Factor the trinomial completely. - $-36 x^{2}-30 x+36$

Factor the trinomial completely. - $x^{2}+4 x y-21 y^{2}$

Factor the polynomial completely - $81 \mathrm{k}^{3} \mathrm{~m}-375 \mathrm{~m}^{4}$

Factor the polynomial completely - $125 a^{3}-64 b^{3}$

Explain why a cubic equation of the form $\mathrm{ax}^{3}+\mathrm{bx} \mathrm{x}^{2}+\mathrm{cx}=0$ must have 0 in its solution set.

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

actor out the greatest common factor. Simplify the factors, if possible - $3(2-x)^{2}-(2-x)^{3}+4(2-x)$

Factor the polynomial completely - $49 x^{6}+84 x^{3}+36$

$5 p^{2}+4 p q-q^{2}$

Factor the polynomial completely - $147 a^{4}-48 b^{2}$

Which one of the following is not a factored form of $-x^{2}+1 x+56$ ?

Solve the equation - $9 t^{3}-49 t=0$

Factor the polynomial - $9 x^{2}+48 x y+64 y^{2}$

Factor by grouping. - $8 y x+9 x+48 y+54$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 6: Factoring

Factor by grouping. - bx+x+b+1b x+x+b+1bx+x+b+1

Find all solutions by factoring. - 2k2=−9k−92 k^{2}=-9 \mathrm{k}-92k2=−9k−9

Factor the polynomial completely - 9x2−24x+16−y29 x^{2}-24 x+16-y^{2}9x2−24x+16−y2

Factor the polynomial completely - 36−(m+2n)236-(m+2 n)^{2}36−(m+2n)2

Factor the polynomial completely - t3+216t^{3}+216t3+216

Solve the equation. - (8y+7)(5y+11)=0(8 y+7)(5 y+11)=0(8y+7)(5y+11)=0

Factor the trinomial completely. - −36x2−30x+36-36 x^{2}-30 x+36−36x2−30x+36

Factor the trinomial completely. - x2+4xy−21y2x^{2}+4 x y-21 y^{2}x2+4xy−21y2

Factor the polynomial completely - 81k3 m−375 m481 \mathrm{k}^{3} \mathrm{~m}-375 \mathrm{~m}^{4}81k3 m−375 m4

Factor the polynomial completely - 125a3−64b3125 a^{3}-64 b^{3}125a3−64b3

Explain why a cubic equation of the form ax3+bxx2+cx=0\mathrm{ax}^{3}+\mathrm{bx} \mathrm{x}^{2}+\mathrm{cx}=0ax3+bxx2+cx=0 must have 0 in its solution set.

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

actor out the greatest common factor. Simplify the factors, if possible - 3(2−x)2−(2−x)3+4(2−x)3(2-x)^{2}-(2-x)^{3}+4(2-x)3(2−x)2−(2−x)3+4(2−x)

Factor the polynomial completely - 49x6+84x3+3649 x^{6}+84 x^{3}+3649x6+84x3+36

5p2+4pq−q25 p^{2}+4 p q-q^{2}5p2+4pq−q2

Factor the polynomial completely - 147a4−48b2147 a^{4}-48 b^{2}147a4−48b2

Which one of the following is not a factored form of −x2+1x+56-x^{2}+1 x+56−x2+1x+56 ?

Solve the equation - 9t3−49t=09 t^{3}-49 t=09t3−49t=0

Factor the polynomial - 9x2+48xy+64y29 x^{2}+48 x y+64 y^{2}9x2+48xy+64y2

Factor by grouping. - 8yx+9x+48y+548 y x+9 x+48 y+548yx+9x+48y+54

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Factor by grouping. - $b x+x+b+1$

Find all solutions by factoring. - $2 k^{2}=-9 \mathrm{k}-9$

Factor the polynomial completely - $9 x^{2}-24 x+16-y^{2}$

Factor the polynomial completely - $36-(m+2 n)^{2}$

Factor the polynomial completely - $t^{3}+216$

Solve the equation. - $(8 y+7)(5 y+11)=0$

Factor the trinomial completely. - $-36 x^{2}-30 x+36$

Factor the trinomial completely. - $x^{2}+4 x y-21 y^{2}$

Factor the polynomial completely - $81 \mathrm{k}^{3} \mathrm{~m}-375 \mathrm{~m}^{4}$

Factor the polynomial completely - $125 a^{3}-64 b^{3}$

Explain why a cubic equation of the form $\mathrm{ax}^{3}+\mathrm{bx} \mathrm{x}^{2}+\mathrm{cx}=0$ must have 0 in its solution set.

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

actor out the greatest common factor. Simplify the factors, if possible - $3(2-x)^{2}-(2-x)^{3}+4(2-x)$

Factor the polynomial completely - $49 x^{6}+84 x^{3}+36$

$5 p^{2}+4 p q-q^{2}$

Factor the polynomial completely - $147 a^{4}-48 b^{2}$

Which one of the following is not a factored form of $-x^{2}+1 x+56$ ?

Solve the equation - $9 t^{3}-49 t=0$

Factor the polynomial - $9 x^{2}+48 x y+64 y^{2}$

Factor by grouping. - $8 y x+9 x+48 y+54$