Question 1

Factor the GCF out of the given expression.
-$10 \mathrm{a}^{6}+40 \mathrm{a}^{4}$

Accepted Answer

A)  $40\left(a^{2}+4 a\right)$ 
B)  $10\left(a^{6}+4 a^{4}\right)$ 
C)  $10 \mathrm{a}^{4}\left(\mathrm{a}^{2}+4\right)$ 
D)  $\mathrm{a}^{4}\left(10 \mathrm{a}^{2}+40\right)$ 
A)  $40\left(a^{2}+4 a\right)$ 
B)  $10\left(a^{6}+4 a^{4}\right)$ 
C)  $10 \mathrm{a}^{4}\left(\mathrm{a}^{2}+4\right)$ 
D)  $\mathrm{a}^{4}\left(10 \mathrm{a}^{2}+40\right)$

Question 2

Factor completely. If the polynomial cannot be factored, write "prime."
-$3 x^{4}-27 x^{3}+24 x^{2}$

Accepted Answer

A)  $3 x^{2}(x-1)(x-8)$ 
B)  $x^{2}(x-1)(3 x-24)$ 
C)  $x^{2}(3 x-3)(x-8)$ 
D)  $3\left(x^{2}-1\right)\left(x^{2}-8\right)$ 
A)  $3 x^{2}(x-1)(x-8)$ 
B)  $x^{2}(x-1)(3 x-24)$ 
C)  $x^{2}(3 x-3)(x-8)$ 
D)  $3\left(x^{2}-1\right)\left(x^{2}-8\right)$

Question 3

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

Accepted Answer

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

Question 4

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(x^{7} y^{9} z^{8}\right)^{4}\left(x^{5} y^{10} z^{12}\right)^{4}$

Accepted Answer

A)  $x^{48} y^{76} z^{80}$ 
B)  $x^{96} {y} ^{152}z^{ 160}$ 
C)  $2 x^{48} 2 y^{76} 2 z ^{80}$ 
D)  $x^{560}{y} ^{1440 }z^{ 1536}$ 
A)  $x^{48} y^{76} z^{80}$ 
B)  $x^{96} {y} ^{152}z^{ 160}$ 
C)  $2 x^{48} 2 y^{76} 2 z ^{80}$ 
D)  $x^{560}{y} ^{1440 }z^{ 1536}$

Question 5

$(x+6 y)(x-9 y)$

Accepted Answer

A)  $x-3 x y-54 y$ 
B)  $x^{2}-3 x y-3 y^{2}$ 
C)  $x^{2}-3 x y-54 y^{2}$ 
D)  $x^{2}-6 x y-54 y^{2}$ 
A)  $x-3 x y-54 y$ 
B)  $x^{2}-3 x y-3 y^{2}$ 
C)  $x^{2}-3 x y-54 y^{2}$ 
D)  $x^{2}-6 x y-54 y^{2}$

Question 6

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}+27$

Accepted Answer

A)  $(x+3)\left(x^{2}-3 x+9\right)$ 
B)  $(x-27)\left(x^{2}-1\right)$ 
C)  $(x+3)\left(x^{2}+9\right)$ 
D)  $(x-3)\left(x^{2}+3 x+9\right)$ 
A)  $(x+3)\left(x^{2}-3 x+9\right)$ 
B)  $(x-27)\left(x^{2}-1\right)$ 
C)  $(x+3)\left(x^{2}+9\right)$ 
D)  $(x-3)\left(x^{2}+3 x+9\right)$

Question 7

Factor completely. If the polynomial cannot be factored, write "prime."
-$8 s^{3}+1$

Accepted Answer

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

Question 8

Evaluate the polynomial or polynomial function for the given value of the variable.
-$-6 x^{2}-6 x-10$ for $x=2$

Accepted Answer

A)  -50 
B)  -46 
C)  -56 
D)  -34 
A)  -50 
B)  -46 
C)  -56 
D)  -34

Question 9

Divide. Assume all variables are nonzero
-$\left(12 x^{8}\right) \div\left(2 x^{2}\right)$

Accepted Answer

A)  $6 x^{10}$ 
B)  $10 x^{6}$ 
C)  36 
D)  $6 x^{6}$ 
A)  $6 x^{10}$ 
B)  $10 x^{6}$ 
C)  36 
D)  $6 x^{6}$

Question 10

Find the missing monomial, factor or term.
-$(?)^{2}=36 x^{2}-12 x+1$

Accepted Answer

A)  $6 x-1$ 
B)  $6 x+1$ 
C)  $x-1$ 
D)  $6 x-6$ 
A)  $6 x-1$ 
B)  $6 x+1$ 
C)  $x-1$ 
D)  $6 x-6$

Question 11

Find the GCF.
-$33,44,77$

Accepted Answer

A)  11 
B)  33 
C)  1 
D)  5 
A)  11 
B)  33 
C)  1 
D)  5

Question 12

Factor by grouping.
-$3 x^{2}+5 x+15 x+25$

Accepted Answer

A)  $(3 x+5)(5 x+3)$ 
B)  $(3 x+5)(3 x+5)$ 
C)  $(x+5)(3 x+5)$ 
D)  $(x-5)(3 x-5)$ 
A)  $(3 x+5)(5 x+3)$ 
B)  $(3 x+5)(3 x+5)$ 
C)  $(x+5)(3 x+5)$ 
D)  $(x-5)(3 x-5)$

Question 13

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{-12,0\}$

Accepted Answer

A)  $x^{2}+12=0$ 
B)  $x^{2}-12=0$ 
C)  $x^{2}-12 x=0$ 
D)  $x^{2}+12 x=0$ 
A)  $x^{2}+12=0$ 
B)  $x^{2}-12=0$ 
C)  $x^{2}-12 x=0$ 
D)  $x^{2}+12 x=0$

Question 14

Factor completely. If the polynomial cannot be factored, write "prime."
-$12 x^{3}+25 x^{2}+12 x$

Accepted Answer

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

Question 15

Factor the GCF out of the given expression.
-$81 x^{8} y^8+54 x^{2} y^{6}-90 x^ 5 y ^3$

Accepted Answer

A)  $9 x\left(9 x^{8} y^8+6 x^{2} y^{6}-10 x^{5} y^{3}\right)$ 
B)  $9 x^{2}\left(9 x^{6} y^8+6 y^{6}-10 x^{3} y^{3}\right)$ 
C)  $9\left(9 x^{8} y^8+6 x^{2} y^{6}-10 x^{5} y 3\right)$ 
D)  $9 x^{2} y^{3}\left(9 x^{6} y^5+6 y^{3}-10 x^{3}\right)$ 
A)  $9 x\left(9 x^{8} y^8+6 x^{2} y^{6}-10 x^{5} y^{3}\right)$ 
B)  $9 x^{2}\left(9 x^{6} y^8+6 y^{6}-10 x^{3} y^{3}\right)$ 
C)  $9\left(9 x^{8} y^8+6 x^{2} y^{6}-10 x^{5} y 3\right)$ 
D)  $9 x^{2} y^{3}\left(9 x^{6} y^5+6 y^{3}-10 x^{3}\right)$

Question 16

Find the special product using the appropriate formula
-$f(x)=x^{3}-3 x^{2}+2 x+7, g(x)=-8 x^{5}$

Accepted Answer

A)  $-8 x^{15}-24 x^{10}+16 x^{6}+56 x^{5}$ 
B)  $-8 x^{8}+24 x^{7}-16 x^{6}-56 x^{5}$ 
C)  $-8 x^{15}+24 x^{10}-16 x^{6}-56 x^{5}$ 
D)  $-8 x^{8}-24 x^{7}+16 x^{6}+56 x^{5}$ 
A)  $-8 x^{15}-24 x^{10}+16 x^{6}+56 x^{5}$ 
B)  $-8 x^{8}+24 x^{7}-16 x^{6}-56 x^{5}$ 
C)  $-8 x^{15}+24 x^{10}-16 x^{6}-56 x^{5}$ 
D)  $-8 x^{8}-24 x^{7}+16 x^{6}+56 x^{5}$

Question 17

$15 x^{2}-3 x=0$

Accepted Answer

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

Question 18

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 17 feet by 22 feet and the area of the rug is 204 square feet, how wide will the border be?

Accepted Answer

A)  5 feet 
B)  2.5 feet 
C)  4.5 feet 
D)  3.5 feet 
A)  5 feet 
B)  2.5 feet 
C)  4.5 feet 
D)  3.5 feet

Question 19

The area of a square lawn is numerically 12 feet more than the perimeter. Find the length of the side.

Accepted Answer

A)  72 feet 
B)  24 feet 
C)  6 feet 
D)  18 feet 
A)  72 feet 
B)  24 feet 
C)  6 feet 
D)  18 feet

Question 20

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}+8 x^{2}-20 x$

Accepted Answer

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

Factor the GCF out of the given expression. - $10 \mathrm{a}^{6}+40 \mathrm{a}^{4}$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{4}-27 x^{3}+24 x^{2}$

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

Choose the one alternative that best completes the statement or answers thequestion. - $\left(x^{7} y^{9} z^{8}\right)^{4}\left(x^{5} y^{10} z^{12}\right)^{4}$

$(x+6 y)(x-9 y)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}+27$

Factor completely. If the polynomial cannot be factored, write "prime." - $8 s^{3}+1$

Evaluate the polynomial or polynomial function for the given value of the variable. - $-6 x^{2}-6 x-10$ for $x=2$

Divide. Assume all variables are nonzero - $\left(12 x^{8}\right) \div\left(2 x^{2}\right)$

Find the missing monomial, factor or term. - $(?)^{2}=36 x^{2}-12 x+1$

Find the GCF. - $33,44,77$

Factor by grouping. - $3 x^{2}+5 x+15 x+25$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{-12,0\}$

Factor completely. If the polynomial cannot be factored, write "prime." - $12 x^{3}+25 x^{2}+12 x$

Factor the GCF out of the given expression. - $81 x^{8} y^8+54 x^{2} y^{6}-90 x^ 5 y ^3$

Find the special product using the appropriate formula - $f(x)=x^{3}-3 x^{2}+2 x+7, g(x)=-8 x^{5}$

$15 x^{2}-3 x=0$

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 17 feet by 22 feet and the area of the rug is 204 square feet, how wide will the border be?

The area of a square lawn is numerically 12 feet more than the perimeter. Find the length of the side.

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}+8 x^{2}-20 x$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents, Polynomials, and Factoring Polynomials

Factor the GCF out of the given expression. - 10a6+40a410 \mathrm{a}^{6}+40 \mathrm{a}^{4}10a6+40a4

Factor completely. If the polynomial cannot be factored, write "prime." - 3x4−27x3+24x23 x^{4}-27 x^{3}+24 x^{2}3x4−27x3+24x2

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

Choose the one alternative that best completes the statement or answers thequestion. - (x7y9z8)4(x5y10z12)4\left(x^{7} y^{9} z^{8}\right)^{4}\left(x^{5} y^{10} z^{12}\right)^{4}(x7y9z8)4(x5y10z12)4

(x+6y)(x−9y)(x+6 y)(x-9 y)(x+6y)(x−9y)

Factor completely. If the polynomial cannot be factored, write "prime." - x3+27x^{3}+27x3+27

Factor completely. If the polynomial cannot be factored, write "prime." - 8s3+18 s^{3}+18s3+1

Evaluate the polynomial or polynomial function for the given value of the variable. - −6x2−6x−10-6 x^{2}-6 x-10−6x2−6x−10 for x=2x=2x=2

Divide. Assume all variables are nonzero - (12x8)÷(2x2)\left(12 x^{8}\right) \div\left(2 x^{2}\right)(12x8)÷(2x2)

Find the missing monomial, factor or term. - (?)2=36x2−12x+1(?)^{2}=36 x^{2}-12 x+1(?)2=36x2−12x+1

Find the GCF. - 33,44,7733,44,7733,44,77

Factor by grouping. - 3x2+5x+15x+253 x^{2}+5 x+15 x+253x2+5x+15x+25

Find a quadratic equation with integer coefficients that has the given solution set. - {−12,0}\{-12,0\}{−12,0}

Factor completely. If the polynomial cannot be factored, write "prime." - 12x3+25x2+12x12 x^{3}+25 x^{2}+12 x12x3+25x2+12x

Factor the GCF out of the given expression. - 81x8y8+54x2y6−90x5y381 x^{8} y^8+54 x^{2} y^{6}-90 x^ 5 y ^381x8y8+54x2y6−90x5y3

Find the special product using the appropriate formula - f(x)=x3−3x2+2x+7,g(x)=−8x5f(x)=x^{3}-3 x^{2}+2 x+7, g(x)=-8 x^{5}f(x)=x3−3x2+2x+7,g(x)=−8x5

15x2−3x=015 x^{2}-3 x=015x2−3x=0

A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 17 feet by 22 feet and the area of the rug is 204 square feet, how wide will the border be?

The area of a square lawn is numerically 12 feet more than the perimeter. Find the length of the side.

Factor completely. If the polynomial cannot be factored, write "prime." - x3+8x2−20xx^{3}+8 x^{2}-20 xx3+8x2−20x

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Factor the GCF out of the given expression. - $10 \mathrm{a}^{6}+40 \mathrm{a}^{4}$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{4}-27 x^{3}+24 x^{2}$

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

Choose the one alternative that best completes the statement or answers thequestion. - $\left(x^{7} y^{9} z^{8}\right)^{4}\left(x^{5} y^{10} z^{12}\right)^{4}$

$(x+6 y)(x-9 y)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}+27$

Factor completely. If the polynomial cannot be factored, write "prime." - $8 s^{3}+1$

Evaluate the polynomial or polynomial function for the given value of the variable. - $-6 x^{2}-6 x-10$ for $x=2$

Divide. Assume all variables are nonzero - $\left(12 x^{8}\right) \div\left(2 x^{2}\right)$

Find the missing monomial, factor or term. - $(?)^{2}=36 x^{2}-12 x+1$

Find the GCF. - $33,44,77$

Factor by grouping. - $3 x^{2}+5 x+15 x+25$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{-12,0\}$

Factor completely. If the polynomial cannot be factored, write "prime." - $12 x^{3}+25 x^{2}+12 x$

Factor the GCF out of the given expression. - $81 x^{8} y^8+54 x^{2} y^{6}-90 x^ 5 y ^3$

Find the special product using the appropriate formula - $f(x)=x^{3}-3 x^{2}+2 x+7, g(x)=-8 x^{5}$

$15 x^{2}-3 x=0$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}+8 x^{2}-20 x$