Question 1

Determine which factoring technique is appropriate for the given polynomial.
-$x^{2}+169$

Accepted Answer

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

Question 2

Factor completely. If the polynomial cannot be factored, write "prime."
-$-8 x^{2}+49 x+49$

Accepted Answer

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

Question 3

Find the missing dividend or divisor
-$\frac{?}{\mathrm{x}}=2 \mathrm{x}^{7}+5 \mathrm{x}^{2}+\mathrm{x}$

Accepted Answer

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

Question 4

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

Accepted Answer

A)  $(x-6)(x+8)$ 
B)  $(x-48)(x+1)$ 
C)  $(x+6)(x-8)$ 
D)  Prime 
A)  $(x-6)(x+8)$ 
B)  $(x-48)(x+1)$ 
C)  $(x+6)(x-8)$ 
D)  Prime

Question 5

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$\frac{a^{6}}{b^{-4}}$

Accepted Answer

A)  1 
B)  $\left(\frac{a}{b}\right)^{2}$ 
C)  $\frac{b^{4}}{a^{6}}$ 
D)  $a^{6} b^{4}$ 
A)  1 
B)  $\left(\frac{a}{b}\right)^{2}$ 
C)  $\frac{b^{4}}{a^{6}}$ 
D)  $a^{6} b^{4}$

Question 6

Determine whether the simplified version of the given expression would be a
-$(x-5)(x+5)$

Accepted Answer

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

Question 7

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}-729$

Accepted Answer

A)  $(x+9)\left(x^{2}-9 x+81\right)$ 
B)  $(x+729)\left(x^{2}-1\right)$ 
C)  $(x-9)\left(x^{2}+81\right)$ 
D)  $(x-9)\left(x^{2}+9 x+81\right)$ 
A)  $(x+9)\left(x^{2}-9 x+81\right)$ 
B)  $(x+729)\left(x^{2}-1\right)$ 
C)  $(x-9)\left(x^{2}+81\right)$ 
D)  $(x-9)\left(x^{2}+9 x+81\right)$

Question 8

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(2 x^{9}\right)^{4}$

Accepted Answer

A)  $16 x^{9}$ 
B)  $16 x^{13}$ 
C)  $2 x^{36}$ 
D)  $16 x^{36}$ 
A)  $16 x^{9}$ 
B)  $16 x^{13}$ 
C)  $2 x^{36}$ 
D)  $16 x^{36}$

Question 9

$\mathrm{x}^{2}-18 \mathrm{x}+81=0$

Accepted Answer

A)  $\{9\}$ 
B)  $\{0,9\}$ 
C)  $\{-9,9\}$ 
D)  $\{9\}$. 
A)  $\{9\}$ 
B)  $\{0,9\}$ 
C)  $\{-9,9\}$ 
D)  $\{9\}$.

Question 10

$(x-7)(8 x+23)=0$

Accepted Answer

A)  $\left\{-7, \frac{8}{23}\right\}$ 
B)  $\left\{-\frac{23}{8}, 7\right\}$ 
C)  $\left\{-\frac{8}{23}, 7\right\}$ 
D)  $\left\{-7, \frac{23}{8}\right\}$ 
A)  $\left\{-7, \frac{8}{23}\right\}$ 
B)  $\left\{-\frac{23}{8}, 7\right\}$ 
C)  $\left\{-\frac{8}{23}, 7\right\}$ 
D)  $\left\{-7, \frac{23}{8}\right\}$

Question 11

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

Accepted Answer

A)  $(x+8)(x-6)$ 
B)  $-(x-8)(x-6)$ 
C)  $-(x-8)(x+6)$ 
D)  Prime 
A)  $(x+8)(x-6)$ 
B)  $-(x-8)(x-6)$ 
C)  $-(x-8)(x+6)$ 
D)  Prime

Question 12

The product of two positive consecutive odd integers is 15 . Find the integers.

Accepted Answer

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

Question 13

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

Accepted Answer

A)  $(x+6)(x+8)$ 
B)  $(x-6)(x-8)$ 
C)  $(x-24)(x-2)$ 
D)  Prime 
A)  $(x+6)(x+8)$ 
B)  $(x-6)(x-8)$ 
C)  $(x-24)(x-2)$ 
D)  Prime

Question 14

Divide. Assume all variables are nonzero
-$\frac{70 x^{9} y^{7}}{10 x^{6} y}$

Accepted Answer

A)  $7 x^{2} y^{7}$ 
B)  $7 x^{3} y^{7}$ 
C)  $60 x^{3} y^{7}$ 
D)  $7 x^{3} y^{6}$ 
A)  $7 x^{2} y^{7}$ 
B)  $7 x^{3} y^{7}$ 
C)  $60 x^{3} y^{7}$ 
D)  $7 x^{3} y^{6}$

Question 15

Factor completely. If the polynomial cannot be factored, write "prime."
-$9 x^{2}-62 x+48$

Accepted Answer

A)  $(9 x-8)(x+6)$ 
B)  $(8-9 x)(9 x-8)$ 
C)  $(9 x-8)(x-6)$ 
D)  $(9 x+40)(9 x-8)$ 
A)  $(9 x-8)(x+6)$ 
B)  $(8-9 x)(9 x-8)$ 
C)  $(9 x-8)(x-6)$ 
D)  $(9 x+40)(9 x-8)$

Question 16

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{-3,2\}$

Accepted Answer

A)  $x^{2}+x-6=0$ 
B)  $x^{2}-5 x+6=0$ 
C)  $x^{2}-x-6=0$ 
D)  $x^{2}+3 x+6=0$ 
A)  $x^{2}+x-6=0$ 
B)  $x^{2}-5 x+6=0$ 
C)  $x^{2}-x-6=0$ 
D)  $x^{2}+3 x+6=0$

Question 17

Perform the indicated calculation. Express your answer using scientific notation.
-$\left(17.05 \times 10^{-9}\right) \div\left(5 \times 10^{3}\right)$

Accepted Answer

A)  $3.41 \times 10^{-12}$ 
B)  $6.82 \times 10^{-6}$ 
C)  $3.41 \times 10^{-6}$ 
D)  $6.82 \times 10^{-12}$ 
A)  $3.41 \times 10^{-12}$ 
B)  $6.82 \times 10^{-6}$ 
C)  $3.41 \times 10^{-6}$ 
D)  $6.82 \times 10^{-12}$

Question 18

$\left(8 m^{2} n-6 m n+4 m n^{2}\right)-\left(4 m^{2} n+4 m n-4 m n^{2}\right)$

Accepted Answer

A)  $4 m^{4} n^{2}-10 m^{2} n^{2}+8 m^{2} n^{4}$ 
B)  $4 m^{4} n^{2}-10 m n+8 m^{2} n^{4}$ 
C)  $4 m^{2} n-10 m n+8 m n^{2}$ 
D)  $4 m^{2} n-2$ 
A)  $4 m^{4} n^{2}-10 m^{2} n^{2}+8 m^{2} n^{4}$ 
B)  $4 m^{4} n^{2}-10 m n+8 m^{2} n^{4}$ 
C)  $4 m^{2} n-10 m n+8 m n^{2}$ 
D)  $4 m^{2} n-2$

Question 19

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

Accepted Answer

A)  $(x+12)(x-5)$ 
B)  $(x-12)(x+1)$ 
C)  $(\mathrm{x}-12)(\mathrm{x}+5)$ 
D)  Prime 
A)  $(x+12)(x-5)$ 
B)  $(x-12)(x+1)$ 
C)  $(\mathrm{x}-12)(\mathrm{x}+5)$ 
D)  Prime

Question 20

Simplify. (A ssume all variables are nonzero.)
-$\left(\frac{\mathrm{a}^{3}}{\mathrm{~b}^{4}}\right)^{2}$

Accepted Answer

A)  $\frac{a^{6}}{b^{8}}$ 
B)  $\frac{a^{6}}{b^{4}}$ 
C)  $\frac{a^{8}}{b^{6}}$ 
D)  $\frac{a^{4}}{b^{8}}$ 
A)  $\frac{a^{6}}{b^{8}}$ 
B)  $\frac{a^{6}}{b^{4}}$ 
C)  $\frac{a^{8}}{b^{6}}$ 
D)  $\frac{a^{4}}{b^{8}}$

Determine which factoring technique is appropriate for the given polynomial. - $x^{2}+169$

Factor completely. If the polynomial cannot be factored, write "prime." - $-8 x^{2}+49 x+49$

Find the missing dividend or divisor - $\frac{?}{\mathrm{x}}=2 \mathrm{x}^{7}+5 \mathrm{x}^{2}+\mathrm{x}$

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

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{a^{6}}{b^{-4}}$

Determine whether the simplified version of the given expression would be a - $(x-5)(x+5)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-729$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(2 x^{9}\right)^{4}$

$\mathrm{x}^{2}-18 \mathrm{x}+81=0$

$(x-7)(8 x+23)=0$

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

The product of two positive consecutive odd integers is 15 . Find the integers.

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

Divide. Assume all variables are nonzero - $\frac{70 x^{9} y^{7}}{10 x^{6} y}$

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}-62 x+48$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{-3,2\}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(17.05 \times 10^{-9}\right) \div\left(5 \times 10^{3}\right)$

$\left(8 m^{2} n-6 m n+4 m n^{2}\right)-\left(4 m^{2} n+4 m n-4 m n^{2}\right)$

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

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{\mathrm{a}^{3}}{\mathrm{~b}^{4}}\right)^{2}$

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

Determine which factoring technique is appropriate for the given polynomial. - x2+169x^{2}+169x2+169

Factor completely. If the polynomial cannot be factored, write "prime." - −8x2+49x+49-8 x^{2}+49 x+49−8x2+49x+49

Find the missing dividend or divisor - ?x=2x7+5x2+x\frac{?}{\mathrm{x}}=2 \mathrm{x}^{7}+5 \mathrm{x}^{2}+\mathrm{x}x?​=2x7+5x2+x

Factor completely. If the polynomial cannot be factored, write "prime." - x2−x−48x^{2}-x-48x2−x−48

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - a6b−4\frac{a^{6}}{b^{-4}}b−4a6​

Determine whether the simplified version of the given expression would be a - (x−5)(x+5)(x-5)(x+5)(x−5)(x+5)

Factor completely. If the polynomial cannot be factored, write "prime." - x3−729x^{3}-729x3−729

Choose the one alternative that best completes the statement or answers thequestion. - (2x9)4\left(2 x^{9}\right)^{4}(2x9)4

x2−18x+81=0\mathrm{x}^{2}-18 \mathrm{x}+81=0x2−18x+81=0

(x−7)(8x+23)=0(x-7)(8 x+23)=0(x−7)(8x+23)=0

Factor completely. If the polynomial cannot be factored, write "prime." - −x2+2x+48-x^{2}+2 x+48−x2+2x+48

The product of two positive consecutive odd integers is 15 . Find the integers.

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

Divide. Assume all variables are nonzero - 70x9y710x6y\frac{70 x^{9} y^{7}}{10 x^{6} y}10x6y70x9y7​

Factor completely. If the polynomial cannot be factored, write "prime." - 9x2−62x+489 x^{2}-62 x+489x2−62x+48

Find a quadratic equation with integer coefficients that has the given solution set. - {−3,2}\{-3,2\}{−3,2}

Perform the indicated calculation. Express your answer using scientific notation. - (17.05×10−9)÷(5×103)\left(17.05 \times 10^{-9}\right) \div\left(5 \times 10^{3}\right)(17.05×10−9)÷(5×103)

(8m2n−6mn+4mn2)−(4m2n+4mn−4mn2)\left(8 m^{2} n-6 m n+4 m n^{2}\right)-\left(4 m^{2} n+4 m n-4 m n^{2}\right)(8m2n−6mn+4mn2)−(4m2n+4mn−4mn2)

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

Simplify. (A ssume all variables are nonzero.) - (a3 b4)2\left(\frac{\mathrm{a}^{3}}{\mathrm{~b}^{4}}\right)^{2}( b4a3​)2

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

Determine which factoring technique is appropriate for the given polynomial. - $x^{2}+169$

Factor completely. If the polynomial cannot be factored, write "prime." - $-8 x^{2}+49 x+49$

Find the missing dividend or divisor - $\frac{?}{\mathrm{x}}=2 \mathrm{x}^{7}+5 \mathrm{x}^{2}+\mathrm{x}$

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

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{a^{6}}{b^{-4}}$

Determine whether the simplified version of the given expression would be a - $(x-5)(x+5)$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-729$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(2 x^{9}\right)^{4}$

$\mathrm{x}^{2}-18 \mathrm{x}+81=0$

$(x-7)(8 x+23)=0$

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

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

Divide. Assume all variables are nonzero - $\frac{70 x^{9} y^{7}}{10 x^{6} y}$

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}-62 x+48$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{-3,2\}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(17.05 \times 10^{-9}\right) \div\left(5 \times 10^{3}\right)$

$\left(8 m^{2} n-6 m n+4 m n^{2}\right)-\left(4 m^{2} n+4 m n-4 m n^{2}\right)$

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

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{\mathrm{a}^{3}}{\mathrm{~b}^{4}}\right)^{2}$