Question 1

Convert the given number to standard notation
-$5.0667 \times 10^{-7}$

Accepted Answer

A)  0.000000050667 
B)  0.00000050667 
C)  0.0000050667 
D)  $-50,667,000$ 
A)  0.000000050667 
B)  0.00000050667 
C)  0.0000050667 
D)  $-50,667,000$

Question 2

Find the GCF.
-$s^{5} t^{3}, s^{2} t^{5}$

Accepted Answer

A)  $s^{7} t^{5}$ 
B)  $s^{2} t^{3}$ 
C)  $s^{5} t^{3}$ 
D)  $s^{2} t^{2}$ 
A)  $s^{7} t^{5}$ 
B)  $s^{2} t^{3}$ 
C)  $s^{5} t^{3}$ 
D)  $s^{2} t^{2}$

Question 3

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}-x^{2}-30$

Accepted Answer

A)  $\left(x^{2}+1\right)\left(x^{2}-30\right)$ 
B)  $\left(x^{2}+5\right)\left(x^{2}-6\right)$ 
C)  $\left(x^{2}+6\right)\left(x^{2}-5\right)$ 
D)  Prime 
A)  $\left(x^{2}+1\right)\left(x^{2}-30\right)$ 
B)  $\left(x^{2}+5\right)\left(x^{2}-6\right)$ 
C)  $\left(x^{2}+6\right)\left(x^{2}-5\right)$ 
D)  Prime

Question 4

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution.
-$x^{2}+7 x-60=0, x=5$

Accepted Answer

A)  $x=12$ 
B)  $x=-5$ 
C)  60 
D)  $x=-12$ 
A)  $x=12$ 
B)  $x=-5$ 
C)  60 
D)  $x=-12$

Question 5

$-3 x^{9} y^8 \cdot 9 x^{8} y$

Accepted Answer

A)  $-27 x^{17} y^{8}$ 
B)  $6 x^{72} y^{8}$ 
C)  $6 x^{17} y^{9}$ 
D)  $-27 x^{17} y^{9}$ 
A)  $-27 x^{17} y^{8}$ 
B)  $6 x^{72} y^{8}$ 
C)  $6 x^{17} y^{9}$ 
D)  $-27 x^{17} y^{9}$

Question 6

Factor completely. If the polynomial cannot be factored, write "prime."
-$5 x^{2}+20 x+20$

Accepted Answer

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

Question 7

Factor completely. If the polynomial cannot be factored, write "prime."
-$18 x^{2}-78 x-60$

Accepted Answer

A)  $(18 x+12)(x-5)$ 
B)  $6(3 x-2)(x+5)$ 
C)  $(3 x+2)(6 x-30)$ 
D)  $6(3 x+2)(x-5)$ 
A)  $(18 x+12)(x-5)$ 
B)  $6(3 x-2)(x+5)$ 
C)  $(3 x+2)(6 x-30)$ 
D)  $6(3 x+2)(x-5)$

Question 8

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}+x^{2}-36 x-36$

Accepted Answer

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

Question 9

Find the missing monomial, factor or term.
-$-3 x^{2} \cdot ?=-15 x^{7}$

Accepted Answer

A)  $-5 x^{5}$ 
B)  $x^{5}$ 
C)  $8 x^{5}$ 
D)  $5 x^{5}$ 
A)  $-5 x^{5}$ 
B)  $x^{5}$ 
C)  $8 x^{5}$ 
D)  $5 x^{5}$

Question 10

Determine which factoring technique is appropriate for the given polynomial.
-$x^{3}+1331 y^{3}$

Accepted Answer

A)  factoring by grouping 
B)  sum of squares 
C)  difference of cubes 
D)  sum of cubes 
A)  factoring by grouping 
B)  sum of squares 
C)  difference of cubes 
D)  sum of cubes

Question 11

For the given functions $f(x)$ and $g(x)$, perform the indicated operation.
-$f(x)=\left(7 x^{5}+6 x^{3}+5\right), g(x)=\left(2 x^{5}-9 x^{3}-3\right)$
Find $f(x)+g(x)$.

Accepted Answer

A)  $7 x^{5}-2 x^{3}+3$ 
B)  $8 x^{8}$ 
C)  $-3 x^{5}+2 x^{3}+9$ 
D)  $9 x^{5}-3 x^{3}+2$ 
A)  $7 x^{5}-2 x^{3}+3$ 
B)  $8 x^{8}$ 
C)  $-3 x^{5}+2 x^{3}+9$ 
D)  $9 x^{5}-3 x^{3}+2$

Question 12

Find the GCF.
-$104 x^{4}, 52 x^{7}$

Accepted Answer

A)  $104 x^{4}$ 
B)  $26 x^{3}$ 
C)  $52 x^{4}$ 
D)  $78 x^{4}$ 
A)  $104 x^{4}$ 
B)  $26 x^{3}$ 
C)  $52 x^{4}$ 
D)  $78 x^{4}$

Question 13

$\left(r^{3}-5 r s+7 s^{2}\right)-\left(3 r^{3}+r s-4 s^{2}\right)$

Accepted Answer

A)  $-3 r^{3}-5 r s+3 s^{2}$ 
B)  $-2 r^{3}-4 r s+11 s^{2}$ 
C)  $-2 r^{3}-6 r s+3 s^{2}$ 
D)  $-2 r^{3}-6 r s+11 s^{2}$ 
A)  $-3 r^{3}-5 r s+3 s^{2}$ 
B)  $-2 r^{3}-4 r s+11 s^{2}$ 
C)  $-2 r^{3}-6 r s+3 s^{2}$ 
D)  $-2 r^{3}-6 r s+11 s^{2}$

Question 14

$x^{2}-x=72$

Accepted Answer

A)  $\{8,-9\}$ 
B)  $\{1,72\}$ 
C)  $\{-8,9\}$ 
D)  $\{8,9\}$ 
A)  $\{8,-9\}$ 
B)  $\{1,72\}$ 
C)  $\{-8,9\}$ 
D)  $\{8,9\}$

Question 15

Factor completely. If the polynomial cannot be factored, write "prime."
-$3 x^{2}-18 x+15$

Accepted Answer

A)  $3(x-1)(x-15)$ 
B)  $3(x+1)(x+5)$ 
C)  $3(x-1)(x-5)$ 
D)  $(3 x-1)(x-15)$ 
A)  $3(x-1)(x-15)$ 
B)  $3(x+1)(x+5)$ 
C)  $3(x-1)(x-5)$ 
D)  $(3 x-1)(x-15)$

Question 16

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\left(3 x^{-4} y^{-4} z^{3}\right)^{-5}$

Accepted Answer

A)  $\frac{x^{20} y^{20}}{243 z 15}$ 
B)  0 
C)  $\frac{3 x^{20} y^{20}}{z^{15}}$ 
D)  $\frac{x^{20} y^{20}}{z^{15}}$ 
A)  $\frac{x^{20} y^{20}}{243 z 15}$ 
B)  0 
C)  $\frac{3 x^{20} y^{20}}{z^{15}}$ 
D)  $\frac{x^{20} y^{20}}{z^{15}}$

Question 17

Evaluate the polynomial
-$x^{2}+2 y^{2}-3 x y$ for $x=2$ and $y=3$

Accepted Answer

A)  4 
B)  40 
C)  -14 
D)  22 
A)  4 
B)  40 
C)  -14 
D)  22

Question 18

Factor completely. If the polynomial cannot be factored, write "prime."
-$5 x^{5}+35 x^{4}+60 x^{3}$

Accepted Answer

A)  $5 x^{3}\left(x^{2}+7 x+12\right)$ 
B)  $x^{3}(x+3)(5 x+20)$ 
C)  $5 x^{3}(x+3)(x+4)$ 
D)  $x^{3}(5 x+15)(x+4)$ 
A)  $5 x^{3}\left(x^{2}+7 x+12\right)$ 
B)  $x^{3}(x+3)(5 x+20)$ 
C)  $5 x^{3}(x+3)(x+4)$ 
D)  $x^{3}(5 x+15)(x+4)$

Question 19

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}+3 x y-18 y^{2}$

Accepted Answer

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

Question 20

Factor completely. If the polynomial cannot be factored, write "prime."
-$10 x^{2}+19 x+6$

Accepted Answer

A)  $(2 x+3)(5 x+2)$ 
B)  $(10 x+3)(x+2)$ 
C)  $(10 x+1)(x-6)$ 
D)  $(2 x-3)(5 x-2)$ 
A)  $(2 x+3)(5 x+2)$ 
B)  $(10 x+3)(x+2)$ 
C)  $(10 x+1)(x-6)$ 
D)  $(2 x-3)(5 x-2)$

Convert the given number to standard notation - $5.0667 \times 10^{-7}$

Find the GCF. - $s^{5} t^{3}, s^{2} t^{5}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-x^{2}-30$

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - $x^{2}+7 x-60=0, x=5$

$-3 x^{9} y^8 \cdot 9 x^{8} y$

Factor completely. If the polynomial cannot be factored, write "prime." - $5 x^{2}+20 x+20$

Factor completely. If the polynomial cannot be factored, write "prime." - $18 x^{2}-78 x-60$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}+x^{2}-36 x-36$

Find the missing monomial, factor or term. - $-3 x^{2} \cdot ?=-15 x^{7}$

Determine which factoring technique is appropriate for the given polynomial. - $x^{3}+1331 y^{3}$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=\left(7 x^{5}+6 x^{3}+5\right), g(x)=\left(2 x^{5}-9 x^{3}-3\right)$ Find $f(x)+g(x)$ .

Find the GCF. - $104 x^{4}, 52 x^{7}$

$\left(r^{3}-5 r s+7 s^{2}\right)-\left(3 r^{3}+r s-4 s^{2}\right)$

$x^{2}-x=72$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{2}-18 x+15$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(3 x^{-4} y^{-4} z^{3}\right)^{-5}$

Evaluate the polynomial - $x^{2}+2 y^{2}-3 x y$ for $x=2$ and $y=3$

Factor completely. If the polynomial cannot be factored, write "prime." - $5 x^{5}+35 x^{4}+60 x^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+3 x y-18 y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $10 x^{2}+19 x+6$

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

Convert the given number to standard notation - 5.0667×10−75.0667 \times 10^{-7}5.0667×10−7

Find the GCF. - s5t3,s2t5s^{5} t^{3}, s^{2} t^{5}s5t3,s2t5

Factor completely. If the polynomial cannot be factored, write "prime." - x3−x2−30x^{3}-x^{2}-30x3−x2−30

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - x2+7x−60=0,x=5x^{2}+7 x-60=0, x=5x2+7x−60=0,x=5

−3x9y8⋅9x8y-3 x^{9} y^8 \cdot 9 x^{8} y−3x9y8⋅9x8y

Factor completely. If the polynomial cannot be factored, write "prime." - 5x2+20x+205 x^{2}+20 x+205x2+20x+20

Factor completely. If the polynomial cannot be factored, write "prime." - 18x2−78x−6018 x^{2}-78 x-6018x2−78x−60

Factor completely. If the polynomial cannot be factored, write "prime." - x3+x2−36x−36x^{3}+x^{2}-36 x-36x3+x2−36x−36

Find the missing monomial, factor or term. - −3x2⋅?=−15x7-3 x^{2} \cdot ?=-15 x^{7}−3x2⋅?=−15x7

Determine which factoring technique is appropriate for the given polynomial. - x3+1331y3x^{3}+1331 y^{3}x3+1331y3

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , perform the indicated operation. - f(x)=(7x5+6x3+5),g(x)=(2x5−9x3−3)f(x)=\left(7 x^{5}+6 x^{3}+5\right), g(x)=\left(2 x^{5}-9 x^{3}-3\right)f(x)=(7x5+6x3+5),g(x)=(2x5−9x3−3) Find f(x)+g(x)f(x)+g(x)f(x)+g(x) .

Find the GCF. - 104x4,52x7104 x^{4}, 52 x^{7}104x4,52x7

(r3−5rs+7s2)−(3r3+rs−4s2)\left(r^{3}-5 r s+7 s^{2}\right)-\left(3 r^{3}+r s-4 s^{2}\right)(r3−5rs+7s2)−(3r3+rs−4s2)

x2−x=72x^{2}-x=72x2−x=72

Factor completely. If the polynomial cannot be factored, write "prime." - 3x2−18x+153 x^{2}-18 x+153x2−18x+15

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (3x−4y−4z3)−5\left(3 x^{-4} y^{-4} z^{3}\right)^{-5}(3x−4y−4z3)−5

Evaluate the polynomial - x2+2y2−3xyx^{2}+2 y^{2}-3 x yx2+2y2−3xy for x=2x=2x=2 and y=3y=3y=3

Factor completely. If the polynomial cannot be factored, write "prime." - 5x5+35x4+60x35 x^{5}+35 x^{4}+60 x^{3}5x5+35x4+60x3

Factor completely. If the polynomial cannot be factored, write "prime." - x2+3xy−18y2x^{2}+3 x y-18 y^{2}x2+3xy−18y2

Factor completely. If the polynomial cannot be factored, write "prime." - 10x2+19x+610 x^{2}+19 x+610x2+19x+6

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

Convert the given number to standard notation - $5.0667 \times 10^{-7}$

Find the GCF. - $s^{5} t^{3}, s^{2} t^{5}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-x^{2}-30$

For the given quadratic equation, one of its solutions has been provided. Use it to find the other solution. - $x^{2}+7 x-60=0, x=5$

$-3 x^{9} y^8 \cdot 9 x^{8} y$

Factor completely. If the polynomial cannot be factored, write "prime." - $5 x^{2}+20 x+20$

Factor completely. If the polynomial cannot be factored, write "prime." - $18 x^{2}-78 x-60$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}+x^{2}-36 x-36$

Find the missing monomial, factor or term. - $-3 x^{2} \cdot ?=-15 x^{7}$

Determine which factoring technique is appropriate for the given polynomial. - $x^{3}+1331 y^{3}$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=\left(7 x^{5}+6 x^{3}+5\right), g(x)=\left(2 x^{5}-9 x^{3}-3\right)$ Find $f(x)+g(x)$ .

Find the GCF. - $104 x^{4}, 52 x^{7}$

$\left(r^{3}-5 r s+7 s^{2}\right)-\left(3 r^{3}+r s-4 s^{2}\right)$

$x^{2}-x=72$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{2}-18 x+15$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(3 x^{-4} y^{-4} z^{3}\right)^{-5}$

Evaluate the polynomial - $x^{2}+2 y^{2}-3 x y$ for $x=2$ and $y=3$

Factor completely. If the polynomial cannot be factored, write "prime." - $5 x^{5}+35 x^{4}+60 x^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+3 x y-18 y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $10 x^{2}+19 x+6$