Question 1

Evaluate the polynomial or polynomial function for the given value of the variable.
-$f(x)=-2 x^{5}+6 x^{4}-2 x^{3}-x^{2}, f(3)$

Accepted Answer

A)  -67 
B)  -34 
C)  -63 
D)  - 68 
A)  -67 
B)  -34 
C)  -63 
D)  - 68

Question 2

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{4}-14 x^{3}+48 x^{2}$

Accepted Answer

A)  $x^{2}(x-6)(x-8)$ 
B)  $x^{2}(x-48)(x-1)$ 
C)  $x^{2}(x+6)(x+8)$ 
D)  $\left(x^{2}-6\right)\left(x^{2}-8\right)$ 
A)  $x^{2}(x-6)(x-8)$ 
B)  $x^{2}(x-48)(x-1)$ 
C)  $x^{2}(x+6)(x+8)$ 
D)  $\left(x^{2}-6\right)\left(x^{2}-8\right)$

Question 3

Divide using long division.
-$\frac{2 x^{2}+8 x-10}{2 x-2}$

Accepted Answer

A)  $x-8$ 
B)  $x-5+\frac{3}{2 x-2}$ 
C)  $x+5+\frac{2}{2 x-2}$ 
D)  $x+5$ 
A)  $x-8$ 
B)  $x-5+\frac{3}{2 x-2}$ 
C)  $x+5+\frac{2}{2 x-2}$ 
D)  $x+5$

Question 4

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-7 x-60$

Accepted Answer

A)  $(x-5)(x+12)$ 
B)  $(x-60)(x+1)$ 
C)  $(x+5)(x-12)$ 
D)  Prime 
A)  $(x-5)(x+12)$ 
B)  $(x-60)(x+1)$ 
C)  $(x+5)(x-12)$ 
D)  Prime

Question 5

$(5 y-4)\left(25 y^{2}+20 y+16\right)$

Accepted Answer

A)  $125 y^{3}-64$ 
B)  $25 y^{3}+64$ 
C)  $125 y^{3}+80 y^{2}-64$ 
D)  $125 y^{3}+64$ 
A)  $125 y^{3}-64$ 
B)  $25 y^{3}+64$ 
C)  $125 y^{3}+80 y^{2}-64$ 
D)  $125 y^{3}+64$

Question 6

A computer can do one calculation in $1.4 \times 10^{-7}$ seconds. How long would it take the computer to do a trillion $\left(10^{12}\right)$ calculations?

Accepted Answer

A)  $1.4 \times 10^{5}$ seconds 
B)  $1.4 \times 10^{6}$ seconds 
C)  $1.4 \times 10^{-6}$ seconds 
D)  $1.4 \times 10^{9}$ seconds 
A)  $1.4 \times 10^{5}$ seconds 
B)  $1.4 \times 10^{6}$ seconds 
C)  $1.4 \times 10^{-6}$ seconds 
D)  $1.4 \times 10^{9}$ seconds

Question 7

The product of two consecutive integers is 9 less than 9 times their sum. Find the integers.

Accepted Answer

A)  $-18,-17$ 
B)  17,18 
C)  0,1 
D)  18,19 
A)  $-18,-17$ 
B)  17,18 
C)  0,1 
D)  18,19

Question 8

A rectangular garden is three times as long as it is wide. If the area of the garden is 867 square feet, find the length and width of the garden.

Accepted Answer

A)  Length: 17 feet; Width: 3 feet 
B)  Length: 51 feet; Width: 17 feet 
C)  Length: 48 feet; Width: 16 feet 
D)  Length: 289 feet; Width: 3 feet 
A)  Length: 17 feet; Width: 3 feet 
B)  Length: 51 feet; Width: 17 feet 
C)  Length: 48 feet; Width: 16 feet 
D)  Length: 289 feet; Width: 3 feet

Question 9

Factor completely. If the polynomial cannot be factored, write "prime."
-$64 x^{3}-125 y^{3}$

Accepted Answer

A)  $(4 x-5 y)\left(16 x^{2}+25 y^{2}\right)$ 
B)  $(64 x-5 y)\left(x^{2}+20 x y+25 y^{2}\right)$ 
C)  $\left(4 x+5 y^{2}\right)\left(16 x^{2}-20 x y+25 y^{2}\right)$ 
D)  $(4 x-5 y)\left(16 x^{2}+20 x y+25 y^{2}\right)$ 
A)  $(4 x-5 y)\left(16 x^{2}+25 y^{2}\right)$ 
B)  $(64 x-5 y)\left(x^{2}+20 x y+25 y^{2}\right)$ 
C)  $\left(4 x+5 y^{2}\right)\left(16 x^{2}-20 x y+25 y^{2}\right)$ 
D)  $(4 x-5 y)\left(16 x^{2}+20 x y+25 y^{2}\right)$

Question 10

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\left(\frac{x^{4} y^{4}}{w z^{5}}\right)^{-4}$

Accepted Answer

A)  $\frac{w z^{20}}{x^{16} y^{16}}$ 
B)  $\frac{x^{16} y^{16}}{w^{4} z^{20}}$ 
C)  $x^{16} y^{16} w^{4} z^{20}$ 
D)  $\frac{w^{4} z^{20}}{x^{16} y^{16}}$ 
A)  $\frac{w z^{20}}{x^{16} y^{16}}$ 
B)  $\frac{x^{16} y^{16}}{w^{4} z^{20}}$ 
C)  $x^{16} y^{16} w^{4} z^{20}$ 
D)  $\frac{w^{4} z^{20}}{x^{16} y^{16}}$

Question 11

Choose the one alternative that best completes the statement or answers thequestion.
-$2^{4} \cdot 2$

Accepted Answer

A)  8 
B)  64 
C)  16 
D)  32 
A)  8 
B)  64 
C)  16 
D)  32

Question 12

Determine which factoring technique is appropriate for the given polynomial.
-$9 x^{2} y^{3}+18 x y^{2}-27 x y$

Accepted Answer

A)  sum of squares 
B)  factoring by grouping 
C)  factor out GCF 
D)  difference of squares 
A)  sum of squares 
B)  factoring by grouping 
C)  factor out GCF 
D)  difference of squares

Question 13

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

Accepted Answer

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

Question 14

Factor completely. If the polynomial cannot be factored, write "prime."
-$5 x^{3}+5 x^{2} y-60 x y^{2}$

Accepted Answer

A)  $5 x(x-3 y)(x+4 y)$ 
B)  $(x-3 y)\left(5 x^{2}+20 x y\right)$ 
C)  $\left(5 x^{2}+15 x y\right)(x-4 y)$ 
D)  $5 x(x+3 y)(x-4 y)$ 
A)  $5 x(x-3 y)(x+4 y)$ 
B)  $(x-3 y)\left(5 x^{2}+20 x y\right)$ 
C)  $\left(5 x^{2}+15 x y\right)(x-4 y)$ 
D)  $5 x(x+3 y)(x-4 y)$

Question 15

Find the missing dividend or divisor
-$\frac{40 x^{7}+20 x^{2}+12 x}{?}=10 x^{6}+5 x+3$

Accepted Answer

A)  $4 x^{2}$ 
B)  $4 \mathrm{x}$ 
C)  $-4 x$ 
D)  -4 
A)  $4 x^{2}$ 
B)  $4 \mathrm{x}$ 
C)  $-4 x$ 
D)  -4

Question 16

Divide. Assume all variables are nonzero
-$-\frac{4 x^{6} y}{20 x^{5} y^{2}}$

Accepted Answer

A)  $-\frac{x}{5 y}$ 
B)  $\frac{x}{5 y}$ 
C)  $-\frac{5 x}{y}$ 
D)  $-\frac{x y}{5}$ 
A)  $-\frac{x}{5 y}$ 
B)  $\frac{x}{5 y}$ 
C)  $-\frac{5 x}{y}$ 
D)  $-\frac{x y}{5}$

Question 17

Simplify. (A ssume all variables are nonzero.)
-$\left(\frac{x^{3}}{y^{3} z^{7}}\right)^{4}$

Accepted Answer

A)  $\frac{x^{12}}{y^{3} z^{28}}$ 
B)  $\frac{x^{12}}{y^{7} z^{28}}$ 
C)  $\frac{x^{12}}{y^{12} z^{28}}$ 
D)  $\frac{x^{7}}{y^{8} z^{11}}$ 
A)  $\frac{x^{12}}{y^{3} z^{28}}$ 
B)  $\frac{x^{12}}{y^{7} z^{28}}$ 
C)  $\frac{x^{12}}{y^{12} z^{28}}$ 
D)  $\frac{x^{7}}{y^{8} z^{11}}$

Question 18

Simplify. (A ssume all variables are nonzero.)
-$\frac{a^{7} b^{3}}{a^{2} b}$

Accepted Answer

A)  $a^{14} b^{3}$ 
B)  $\frac{21}{2}$ 
C)  $\mathrm{a}^{5} \mathrm{~b}^{2}$ 
D)  $(\mathrm{ab})^{12}$ 
A)  $a^{14} b^{3}$ 
B)  $\frac{21}{2}$ 
C)  $\mathrm{a}^{5} \mathrm{~b}^{2}$ 
D)  $(\mathrm{ab})^{12}$

Question 19

Factor the GCF out of the given expression.
-$2 x(x-4)-3(x-4)$

Accepted Answer

A)  $(10 x-3)(x-4)$ 
B)  $(2 x-3)(x+4)$ 
C)  $(2 x-3)(x-4)$ 
D)  $(2 x+3)(x-4)$ 
A)  $(10 x-3)(x-4)$ 
B)  $(2 x-3)(x+4)$ 
C)  $(2 x-3)(x-4)$ 
D)  $(2 x+3)(x-4)$

Question 20

Divide. Assume all variables are nonzero
-$\frac{42 m^{7} n-12 m^{6} n^{5}+36 m^{5} n^{7}}{6 m^{4} n}$

Accepted Answer

A)  $7 m^{11}-2 m^{10} n^{6}+6 m^{9} n^{8}$ 
B)  $7 m^{3}-2 m^{2} n^{4}+6 m n^{6}$ 
C)  $7 m^{3}-12 m 6 n^{5}+36 m^{5} n^{7}$ 
D)  35 
A)  $7 m^{11}-2 m^{10} n^{6}+6 m^{9} n^{8}$ 
B)  $7 m^{3}-2 m^{2} n^{4}+6 m n^{6}$ 
C)  $7 m^{3}-12 m 6 n^{5}+36 m^{5} n^{7}$ 
D)  35

Evaluate the polynomial or polynomial function for the given value of the variable. - $f(x)=-2 x^{5}+6 x^{4}-2 x^{3}-x^{2}, f(3)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4}-14 x^{3}+48 x^{2}$

Divide using long division. - $\frac{2 x^{2}+8 x-10}{2 x-2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-7 x-60$

$(5 y-4)\left(25 y^{2}+20 y+16\right)$

A computer can do one calculation in $1.4 \times 10^{-7}$ seconds. How long would it take the computer to do a trillion $\left(10^{12}\right)$ calculations?

The product of two consecutive integers is 9 less than 9 times their sum. Find the integers.

A rectangular garden is three times as long as it is wide. If the area of the garden is 867 square feet, find the length and width of the garden.

Factor completely. If the polynomial cannot be factored, write "prime." - $64 x^{3}-125 y^{3}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(\frac{x^{4} y^{4}}{w z^{5}}\right)^{-4}$

Choose the one alternative that best completes the statement or answers thequestion. - $2^{4} \cdot 2$

Determine which factoring technique is appropriate for the given polynomial. - $9 x^{2} y^{3}+18 x y^{2}-27 x y$

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

Factor completely. If the polynomial cannot be factored, write "prime." - $5 x^{3}+5 x^{2} y-60 x y^{2}$

Find the missing dividend or divisor - $\frac{40 x^{7}+20 x^{2}+12 x}{?}=10 x^{6}+5 x+3$

Divide. Assume all variables are nonzero - $-\frac{4 x^{6} y}{20 x^{5} y^{2}}$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{x^{3}}{y^{3} z^{7}}\right)^{4}$

Simplify. (A ssume all variables are nonzero.) - $\frac{a^{7} b^{3}}{a^{2} b}$

Factor the GCF out of the given expression. - $2 x(x-4)-3(x-4)$

Divide. Assume all variables are nonzero - $\frac{42 m^{7} n-12 m^{6} n^{5}+36 m^{5} n^{7}}{6 m^{4} n}$

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

Evaluate the polynomial or polynomial function for the given value of the variable. - f(x)=−2x5+6x4−2x3−x2,f(3)f(x)=-2 x^{5}+6 x^{4}-2 x^{3}-x^{2}, f(3)f(x)=−2x5+6x4−2x3−x2,f(3)

Factor completely. If the polynomial cannot be factored, write "prime." - x4−14x3+48x2x^{4}-14 x^{3}+48 x^{2}x4−14x3+48x2

Divide using long division. - 2x2+8x−102x−2\frac{2 x^{2}+8 x-10}{2 x-2}2x−22x2+8x−10​

Factor completely. If the polynomial cannot be factored, write "prime." - x2−7x−60x^{2}-7 x-60x2−7x−60

(5y−4)(25y2+20y+16)(5 y-4)\left(25 y^{2}+20 y+16\right)(5y−4)(25y2+20y+16)

A computer can do one calculation in 1.4×10−71.4 \times 10^{-7}1.4×10−7 seconds. How long would it take the computer to do a trillion (1012)\left(10^{12}\right)(1012) calculations?

The product of two consecutive integers is 9 less than 9 times their sum. Find the integers.

A rectangular garden is three times as long as it is wide. If the area of the garden is 867 square feet, find the length and width of the garden.

Factor completely. If the polynomial cannot be factored, write "prime." - 64x3−125y364 x^{3}-125 y^{3}64x3−125y3

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (x4y4wz5)−4\left(\frac{x^{4} y^{4}}{w z^{5}}\right)^{-4}(wz5x4y4​)−4

Choose the one alternative that best completes the statement or answers thequestion. - 24⋅22^{4} \cdot 224⋅2

Determine which factoring technique is appropriate for the given polynomial. - 9x2y3+18xy2−27xy9 x^{2} y^{3}+18 x y^{2}-27 x y9x2y3+18xy2−27xy

Factor completely. If the polynomial cannot be factored, write "prime." - 8p3−18 p^{3}-18p3−1

Factor completely. If the polynomial cannot be factored, write "prime." - 5x3+5x2y−60xy25 x^{3}+5 x^{2} y-60 x y^{2}5x3+5x2y−60xy2

Find the missing dividend or divisor - 40x7+20x2+12x?=10x6+5x+3\frac{40 x^{7}+20 x^{2}+12 x}{?}=10 x^{6}+5 x+3?40x7+20x2+12x​=10x6+5x+3

Divide. Assume all variables are nonzero - −4x6y20x5y2-\frac{4 x^{6} y}{20 x^{5} y^{2}}−20x5y24x6y​

Simplify. (A ssume all variables are nonzero.) - (x3y3z7)4\left(\frac{x^{3}}{y^{3} z^{7}}\right)^{4}(y3z7x3​)4

Simplify. (A ssume all variables are nonzero.) - a7b3a2b\frac{a^{7} b^{3}}{a^{2} b}a2ba7b3​

Factor the GCF out of the given expression. - 2x(x−4)−3(x−4)2 x(x-4)-3(x-4)2x(x−4)−3(x−4)

Divide. Assume all variables are nonzero - 42m7n−12m6n5+36m5n76m4n\frac{42 m^{7} n-12 m^{6} n^{5}+36 m^{5} n^{7}}{6 m^{4} n}6m4n42m7n−12m6n5+36m5n7​

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

Evaluate the polynomial or polynomial function for the given value of the variable. - $f(x)=-2 x^{5}+6 x^{4}-2 x^{3}-x^{2}, f(3)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4}-14 x^{3}+48 x^{2}$

Divide using long division. - $\frac{2 x^{2}+8 x-10}{2 x-2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-7 x-60$

$(5 y-4)\left(25 y^{2}+20 y+16\right)$

A computer can do one calculation in $1.4 \times 10^{-7}$ seconds. How long would it take the computer to do a trillion $\left(10^{12}\right)$ calculations?

Factor completely. If the polynomial cannot be factored, write "prime." - $64 x^{3}-125 y^{3}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(\frac{x^{4} y^{4}}{w z^{5}}\right)^{-4}$

Choose the one alternative that best completes the statement or answers thequestion. - $2^{4} \cdot 2$

Determine which factoring technique is appropriate for the given polynomial. - $9 x^{2} y^{3}+18 x y^{2}-27 x y$

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

Factor completely. If the polynomial cannot be factored, write "prime." - $5 x^{3}+5 x^{2} y-60 x y^{2}$

Find the missing dividend or divisor - $\frac{40 x^{7}+20 x^{2}+12 x}{?}=10 x^{6}+5 x+3$

Divide. Assume all variables are nonzero - $-\frac{4 x^{6} y}{20 x^{5} y^{2}}$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{x^{3}}{y^{3} z^{7}}\right)^{4}$

Simplify. (A ssume all variables are nonzero.) - $\frac{a^{7} b^{3}}{a^{2} b}$

Factor the GCF out of the given expression. - $2 x(x-4)-3(x-4)$

Divide. Assume all variables are nonzero - $\frac{42 m^{7} n-12 m^{6} n^{5}+36 m^{5} n^{7}}{6 m^{4} n}$