Question 1

Factor the GCF out of the given expression.
-$x(3 x+2)-6(3 x+2)$

Accepted Answer

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

Question 2

Determine whether the simplified version of the given expression would be a
-$\left(x^{2}+7 x-10\right)+\left(3 x^{2}+x+4\right)$

Accepted Answer

A)  polynomial with four or more terms 
B)  trinomial 
C)  binomial 
A)  polynomial with four or more terms 
B)  trinomial 
C)  binomial

Question 3

Simplify. (A ssume all variables are nonzero.)
-$\frac{(a-7 b)^{20}}{(a-7 b)^{10}}$

Accepted Answer

A)  $(a-7 b)^{10}$ 
B)  $(\mathrm{a}-7 \mathrm{~b})^{200}$ 
C)  $(\mathrm{a}-7 \mathrm{~b})^{30}$ 
D)  $(\mathrm{a}-7 \mathrm{~b})^{2}$ 
A)  $(a-7 b)^{10}$ 
B)  $(\mathrm{a}-7 \mathrm{~b})^{200}$ 
C)  $(\mathrm{a}-7 \mathrm{~b})^{30}$ 
D)  $(\mathrm{a}-7 \mathrm{~b})^{2}$

Question 4

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(3 x^{4} y^{4}\right)\left(4 x^{6} y^{4}\right)$

Accepted Answer

A)  $7 x^{10} y^{8}$ 
B)  $12 x^{24} y ^{16}$ 
C)  $12 x^{10} y^{8}$ 
D)  $7 x^{24} y ^{16}$ 
A)  $7 x^{10} y^{8}$ 
B)  $12 x^{24} y ^{16}$ 
C)  $12 x^{10} y^{8}$ 
D)  $7 x^{24} y ^{16}$

Question 5

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$\frac{9 a^{-3} b^{-8}}{c^{-3} d^{4}}$

Accepted Answer

A)  $\frac{1}{9 a^{3} b^{8} c^{3} d^{4}}$ 
B)  $\frac{9 c^{3} d^{4}}{a^{3} b^{8}}$ 
C)  $\frac{9 c^{3}}{a^{3} b^{8} d^{4}}$ 
D)  $\frac{c^{3}}{9 a^{3} b^{8} d^{4}}$ 
A)  $\frac{1}{9 a^{3} b^{8} c^{3} d^{4}}$ 
B)  $\frac{9 c^{3} d^{4}}{a^{3} b^{8}}$ 
C)  $\frac{9 c^{3}}{a^{3} b^{8} d^{4}}$ 
D)  $\frac{c^{3}}{9 a^{3} b^{8} d^{4}}$

Question 6

$-8(5 x+7)$

Accepted Answer

A)  $8 x$ 
B)  $-40 x+7$ 
C)  $-40 x+56$ 
D)  $-40 x-56$ 
A)  $8 x$ 
B)  $-40 x+7$ 
C)  $-40 x+56$ 
D)  $-40 x-56$

Question 7

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-14 x+45$

Accepted Answer

A)  $(x+9)(x-5)$ 
B)  $(x-9)(x+5)$ 
C)  $(x-9)(x-5)$ 
D)  $(x+9)(x+5)$ 
A)  $(x+9)(x-5)$ 
B)  $(x-9)(x+5)$ 
C)  $(x-9)(x-5)$ 
D)  $(x+9)(x+5)$

Question 8

Factor completely. If the polynomial cannot be factored, write "prime."
-$z^{5}-625 z$

Accepted Answer

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

Question 9

Find the missing monomial, factor or term.
-$(13 x+1) \cdot ?=169 x^{2}-1$

Accepted Answer

A)  $13 x-1$ 
B)  $x-1$ 
C)  $13 x+13$ 
D)  $13 x+1$ 
A)  $13 x-1$ 
B)  $x-1$ 
C)  $13 x+13$ 
D)  $13 x+1$

Question 10

Round your answer to the nearest whole number, if necessary.
-The distance in feet it takes a car traveling at $\mathrm{x} m$ ph to come to a full stop after hitting the brakes is given by the function $f(x)=1.26 x^{2}+0.058 x$. Find the stopping distance for a speed of $40 \mathrm{mph}$. Round to the nearest foot.

Accepted Answer

A)  2039 feet 
B)  2018 feet 
C)  2009 feet 
D)  2 feet 
A)  2039 feet 
B)  2018 feet 
C)  2009 feet 
D)  2 feet

Question 11

Evaluate the polynomial
-$-x y z+x^{5}+z^{4}$ for $x=2, y=-2$ and $z=2$

Accepted Answer

A)  64 
B)  56 
C)  40 
D)  72 
A)  64 
B)  56 
C)  40 
D)  72

Question 12

Simplify. (A ssume all variables are nonzero.)
-$\left(\frac{5 x^{6} y^{2}}{7 z^{6}}\right)^{3}$

Accepted Answer

A)  $\frac{125 x^{18} y^{6}}{343 z^{18}}$ 
B)  $\frac{125 x^{18} y^ 5}{343 z^{18}}$ 
C)  $\frac{125 x^{9} y^{5}}{343 z^{9}}$ 
D)  $\frac{125 x^{18} y^{6}}{7 z^{9}}$ 
A)  $\frac{125 x^{18} y^{6}}{343 z^{18}}$ 
B)  $\frac{125 x^{18} y^ 5}{343 z^{18}}$ 
C)  $\frac{125 x^{9} y^{5}}{343 z^{9}}$ 
D)  $\frac{125 x^{18} y^{6}}{7 z^{9}}$

Question 13

The product of two negative consecutive integers is 19 more than their sum. Find the integers.

Accepted Answer

A)  5, 6 
B)  $-5,-4$ 
C)  $-4,-3$ 
D)  4,5 
A)  5, 6 
B)  $-5,-4$ 
C)  $-4,-3$ 
D)  4,5

Question 14

$\left(2 x^{8}-9 x^{6}+8 x^{2}+4\right)+\left(8 x^{7}+5 x^{6}-4 x\right)$

Accepted Answer

A)  $10 x^{8}-14 x^{6}+8 x^{2}-4 x+4$ 
B)  $2 x^{8}+8 x^{7}-4 x^{6}+8 x^{2}-4 x+4$ 
C)  $2 x^{8}+8 x^{7}+4 x^{6}+8 x^{2}-4 x+4$ 
D)  $10 x^{8}-4 x^{6}+8 x^{2}-4 x+4$ 
A)  $10 x^{8}-14 x^{6}+8 x^{2}-4 x+4$ 
B)  $2 x^{8}+8 x^{7}-4 x^{6}+8 x^{2}-4 x+4$ 
C)  $2 x^{8}+8 x^{7}+4 x^{6}+8 x^{2}-4 x+4$ 
D)  $10 x^{8}-4 x^{6}+8 x^{2}-4 x+4$

Question 15

Find the GCF.
-54, 90, 162

Accepted Answer

A)  14 
B)  6 
C)  18 
D)  2 
A)  14 
B)  6 
C)  18 
D)  2

Question 16

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-10 x y+25 y^{2}$

Accepted Answer

A)  $(x-5 y)(x+5 y)$ 
B)  $(x+5 y)^{2}$ 
C)  Prime 
D)  $(x-5 y)^{2}$ 
A)  $(x-5 y)(x+5 y)$ 
B)  $(x+5 y)^{2}$ 
C)  Prime 
D)  $(x-5 y)^{2}$

Question 17

Factor completely. If the polynomial cannot be factored, write "prime."
-$64 \mathrm{x}^{2}-196$

Accepted Answer

A)  $4(4 x-7)^{2}$ 
B)  $4(4 x+7)(4 x-7)$ 
C)  $(16 x+28)(4 x-7)$ 
D)  $(4 x+7)(16 x-28)$ 
A)  $4(4 x-7)^{2}$ 
B)  $4(4 x+7)(4 x-7)$ 
C)  $(16 x+28)(4 x-7)$ 
D)  $(4 x+7)(16 x-28)$

Question 18

Simplify. (A ssume all variables are nonzero.)
-$(-9)^{0}$

Accepted Answer

A)  1 
B)  -9 
C)  - 1 
D)  0 
A)  1 
B)  -9 
C)  - 1 
D)  0

Question 19

Factor completely. If the polynomial cannot be factored, write "prime."
-$98 x^{4}-50 y^{2}$

Accepted Answer

A)  $2\left(7 x^{2}+5 y\right)\left(7 x^{2}-5 y\right)$ 
B)  $\left(14 x^{2}+10 y\right)\left(7 x^{2}-5 y\right)$ 
C)  $2\left(7 x^{2}+5 y\right)^{2}$ 
D)  $2\left(7 x^{2}-5 y\right)^{2}$ 
A)  $2\left(7 x^{2}+5 y\right)\left(7 x^{2}-5 y\right)$ 
B)  $\left(14 x^{2}+10 y\right)\left(7 x^{2}-5 y\right)$ 
C)  $2\left(7 x^{2}+5 y\right)^{2}$ 
D)  $2\left(7 x^{2}-5 y\right)^{2}$

Question 20

$-2 y\left(-4 y^{8}\right)$

Accepted Answer

A)  $-6 y^{8}$ 
B)  $8 y^{9}$ 
C)  $-8 y^{9}$ 
D)  $2 y-4 y^{8}$ 
A)  $-6 y^{8}$ 
B)  $8 y^{9}$ 
C)  $-8 y^{9}$ 
D)  $2 y-4 y^{8}$

Factor the GCF out of the given expression. - $x(3 x+2)-6(3 x+2)$

Determine whether the simplified version of the given expression would be a - $\left(x^{2}+7 x-10\right)+\left(3 x^{2}+x+4\right)$

Simplify. (A ssume all variables are nonzero.) - $\frac{(a-7 b)^{20}}{(a-7 b)^{10}}$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(3 x^{4} y^{4}\right)\left(4 x^{6} y^{4}\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{9 a^{-3} b^{-8}}{c^{-3} d^{4}}$

$-8(5 x+7)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-14 x+45$

Factor completely. If the polynomial cannot be factored, write "prime." - $z^{5}-625 z$

Find the missing monomial, factor or term. - $(13 x+1) \cdot ?=169 x^{2}-1$

Evaluate the polynomial - $-x y z+x^{5}+z^{4}$ for $x=2, y=-2$ and $z=2$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{5 x^{6} y^{2}}{7 z^{6}}\right)^{3}$

The product of two negative consecutive integers is 19 more than their sum. Find the integers.

$\left(2 x^{8}-9 x^{6}+8 x^{2}+4\right)+\left(8 x^{7}+5 x^{6}-4 x\right)$

Find the GCF. -54, 90, 162

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-10 x y+25 y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $64 \mathrm{x}^{2}-196$

Simplify. (A ssume all variables are nonzero.) - $(-9)^{0}$

Factor completely. If the polynomial cannot be factored, write "prime." - $98 x^{4}-50 y^{2}$

$-2 y\left(-4 y^{8}\right)$

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. - x(3x+2)−6(3x+2)x(3 x+2)-6(3 x+2)x(3x+2)−6(3x+2)

Determine whether the simplified version of the given expression would be a - (x2+7x−10)+(3x2+x+4)\left(x^{2}+7 x-10\right)+\left(3 x^{2}+x+4\right)(x2+7x−10)+(3x2+x+4)

Simplify. (A ssume all variables are nonzero.) - (a−7b)20(a−7b)10\frac{(a-7 b)^{20}}{(a-7 b)^{10}}(a−7b)10(a−7b)20​

Choose the one alternative that best completes the statement or answers thequestion. - (3x4y4)(4x6y4)\left(3 x^{4} y^{4}\right)\left(4 x^{6} y^{4}\right)(3x4y4)(4x6y4)

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - 9a−3b−8c−3d4\frac{9 a^{-3} b^{-8}}{c^{-3} d^{4}}c−3d49a−3b−8​

−8(5x+7)-8(5 x+7)−8(5x+7)

Factor completely. If the polynomial cannot be factored, write "prime." - x2−14x+45x^{2}-14 x+45x2−14x+45

Factor completely. If the polynomial cannot be factored, write "prime." - z5−625zz^{5}-625 zz5−625z

Find the missing monomial, factor or term. - (13x+1)⋅?=169x2−1(13 x+1) \cdot ?=169 x^{2}-1(13x+1)⋅?=169x2−1

Evaluate the polynomial - −xyz+x5+z4-x y z+x^{5}+z^{4}−xyz+x5+z4 for x=2,y=−2x=2, y=-2x=2,y=−2 and z=2z=2z=2

Simplify. (A ssume all variables are nonzero.) - (5x6y27z6)3\left(\frac{5 x^{6} y^{2}}{7 z^{6}}\right)^{3}(7z65x6y2​)3

The product of two negative consecutive integers is 19 more than their sum. Find the integers.

(2x8−9x6+8x2+4)+(8x7+5x6−4x)\left(2 x^{8}-9 x^{6}+8 x^{2}+4\right)+\left(8 x^{7}+5 x^{6}-4 x\right)(2x8−9x6+8x2+4)+(8x7+5x6−4x)

Find the GCF. -54, 90, 162

Factor completely. If the polynomial cannot be factored, write "prime." - x2−10xy+25y2x^{2}-10 x y+25 y^{2}x2−10xy+25y2

Factor completely. If the polynomial cannot be factored, write "prime." - 64x2−19664 \mathrm{x}^{2}-19664x2−196

Simplify. (A ssume all variables are nonzero.) - (−9)0(-9)^{0}(−9)0

Factor completely. If the polynomial cannot be factored, write "prime." - 98x4−50y298 x^{4}-50 y^{2}98x4−50y2

−2y(−4y8)-2 y\left(-4 y^{8}\right)−2y(−4y8)

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. - $x(3 x+2)-6(3 x+2)$

Determine whether the simplified version of the given expression would be a - $\left(x^{2}+7 x-10\right)+\left(3 x^{2}+x+4\right)$

Simplify. (A ssume all variables are nonzero.) - $\frac{(a-7 b)^{20}}{(a-7 b)^{10}}$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(3 x^{4} y^{4}\right)\left(4 x^{6} y^{4}\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{9 a^{-3} b^{-8}}{c^{-3} d^{4}}$

$-8(5 x+7)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-14 x+45$

Factor completely. If the polynomial cannot be factored, write "prime." - $z^{5}-625 z$

Find the missing monomial, factor or term. - $(13 x+1) \cdot ?=169 x^{2}-1$

Evaluate the polynomial - $-x y z+x^{5}+z^{4}$ for $x=2, y=-2$ and $z=2$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{5 x^{6} y^{2}}{7 z^{6}}\right)^{3}$

$\left(2 x^{8}-9 x^{6}+8 x^{2}+4\right)+\left(8 x^{7}+5 x^{6}-4 x\right)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-10 x y+25 y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $64 \mathrm{x}^{2}-196$

Simplify. (A ssume all variables are nonzero.) - $(-9)^{0}$

Factor completely. If the polynomial cannot be factored, write "prime." - $98 x^{4}-50 y^{2}$

$-2 y\left(-4 y^{8}\right)$