Question 1

Determine which factoring technique is appropriate for the given polynomial.
-$x^{3}-8 x^{2}-7 x+56$

Accepted Answer

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

Question 2

Find the GCF.
-9, 18, 24

Accepted Answer

A)  3 
B)  6 
C)  1 
D)  9 
A)  3 
B)  6 
C)  1 
D)  9

Question 3

$\left(6 x^{8}-7 x^{6}+5 x^{2}+9\right)+\left(6 x^{7}+3 x^{6}-5 x\right)$

Accepted Answer

A)  $6 x^{8}+6 x^{7}-4 x^{6}+5 x^{2}-5 x+9$ 
B)  $12 x^{8}-4 x^{6}+5 x^{2}-5 x+9$ 
C)  $12 x^{8}-10 x^{6}+5 x^{2}-5 x+9$ 
D)  $6 x^{8}+6 x^{7}+4 x^{6}+5 x^{2}-5 x+9$ 
A)  $6 x^{8}+6 x^{7}-4 x^{6}+5 x^{2}-5 x+9$ 
B)  $12 x^{8}-4 x^{6}+5 x^{2}-5 x+9$ 
C)  $12 x^{8}-10 x^{6}+5 x^{2}-5 x+9$ 
D)  $6 x^{8}+6 x^{7}+4 x^{6}+5 x^{2}-5 x+9$

Question 4

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

Accepted Answer

A)  $11 x^{5}$ 
B)  $24 x^{6}$ 
C)  $11 x^{6}$ 
D)  $24 x^{5}$ 
A)  $11 x^{5}$ 
B)  $24 x^{6}$ 
C)  $11 x^{6}$ 
D)  $24 x^{5}$

Question 5

Factor the GCF out of the given expression.
-$20 x^{8}+20 x$

Accepted Answer

A)  $20 x\left(x^{7}+1\right)$ 
B)  $20\left(x^{9}+1\right)$ 
C)  $20 x\left(x^{7}\right)$ 
D)  $20\left(x^{8}+x\right)$ 
A)  $20 x\left(x^{7}+1\right)$ 
B)  $20\left(x^{9}+1\right)$ 
C)  $20 x\left(x^{7}\right)$ 
D)  $20\left(x^{8}+x\right)$

Question 6

Factor by grouping.
-$x^{3}-x^{2}+10 x-10$

Accepted Answer

A)  $\left(x^{2}-10\right)(x+1)$ 
B)  $\left(x^{2}-1\right)(x+10)$ 
C)  $\left(x^{2}+10\right)(x-1)$ 
D)  $\left(x^{2}+1\right)(x-10)$ 
A)  $\left(x^{2}-10\right)(x+1)$ 
B)  $\left(x^{2}-1\right)(x+10)$ 
C)  $\left(x^{2}+10\right)(x-1)$ 
D)  $\left(x^{2}+1\right)(x-10)$

Question 7

The national debt of a small country is $\$ 7,740,000,000$ and the population is $2,396,000$. What is the amount of debt per person?

Accepted Answer

A)  $\$ 32$ 
B)  $\$ 3.2$ 
C)  $\$ 3.2 \times 10^{6}$ 
D)  $\$ 3.2 \times 10^{3}$ 
A)  $\$ 32$ 
B)  $\$ 3.2$ 
C)  $\$ 3.2 \times 10^{6}$ 
D)  $\$ 3.2 \times 10^{3}$

Question 8

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{4}-1$

Accepted Answer

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

Question 9

Divide. Assume all variables are nonzero
-$\left(16 \mathrm{x}^{3}+24 \mathrm{x}^{2}+12 \mathrm{x}\right) \div(4 \mathrm{x})$

Accepted Answer

A)  $4 x^{4}+6 x^{3}+3 x^{2}$ 
B)  27 
C)  $4 x^{2}+9 x$ 
D)  $4 x^{2}+6 x+3$ 
A)  $4 x^{4}+6 x^{3}+3 x^{2}$ 
B)  27 
C)  $4 x^{2}+9 x$ 
D)  $4 x^{2}+6 x+3$

Question 10

$(4 \mathrm{x}+10)(\mathrm{x}-10)$

Accepted Answer

A)  $4 x^{2}+30 x-100$ 
B)  $x^{2}-100 x-30$ 
C)  $x^{2}-30 x-31$ 
D)  $4 x^{2}-30 x-100$ 
A)  $4 x^{2}+30 x-100$ 
B)  $x^{2}-100 x-30$ 
C)  $x^{2}-30 x-31$ 
D)  $4 x^{2}-30 x-100$

Question 11

Determine which factoring technique is appropriate for the given polynomial.
-$24 x^{2}-30 x+6$

Accepted Answer

A)  factoring by grouping 
B)  trinomial, leading coefficient of 1 
C)  factor out GCF 
D)  trinomial, leading coefficient other than 1 
A)  factoring by grouping 
B)  trinomial, leading coefficient of 1 
C)  factor out GCF 
D)  trinomial, leading coefficient other than 1

Question 12

$\left(8 x^{4}-4 x^{3}-9 x^{2}+2\right)-\left(2 x^{4}+6 x^{3}-6 x^{2}-5\right)$

Accepted Answer

A)  $10 x^{4}+2 x^{3}-15 x^{2}-3$ 
B)  $6 x^{4}-2 x^{3}+15 x^{2}-3$ 
C)  $6 x^{4}-10 x^{3}-3 x^{2}+7$ 
D)  $10 x^{4}+2 x^{3}-15 x^{2}+7$ 
A)  $10 x^{4}+2 x^{3}-15 x^{2}-3$ 
B)  $6 x^{4}-2 x^{3}+15 x^{2}-3$ 
C)  $6 x^{4}-10 x^{3}-3 x^{2}+7$ 
D)  $10 x^{4}+2 x^{3}-15 x^{2}+7$

Question 13

Find the number of molecules in the given quantity of a compound whose molar mass is given. Express your answer in scientific notation, rounding the decimal part to the nearest hundredth.
-50 grams of carbon monoxide (CO); molar mass: 28.01 grams

Accepted Answer

A)  $1.07 \times 10^{23}$ molecules 
B)  $8.43 \times 10^{26}$ molecules 
C)  $8.43 \times 10^{27}$ molecules 
D)  $1.07 \times 10^{24}$ molecules 
A)  $1.07 \times 10^{23}$ molecules 
B)  $8.43 \times 10^{26}$ molecules 
C)  $8.43 \times 10^{27}$ molecules 
D)  $1.07 \times 10^{24}$ molecules

Question 14

$\left(-4 m n+4 m n^{2}-2 m^{2} n^{2}\right)+\left(5 m^{2} n+12 m^{2} n^{2}-5 m n\right)$

Accepted Answer

A)  $-9 m n+9 m^{2} n+10 m^{2} n^{2}$ 
B)  $1 m n+4 m n^{2}+5 m^{2} n+10 m^{2} n^{2}$ 
C)  $10 \mathrm{~m}^{2} \mathrm{n}^{2}$ 
D)  $10 m^{2} n^{2}+5 m^{2} n+4 m n^{2}-9 m n$ 
A)  $-9 m n+9 m^{2} n+10 m^{2} n^{2}$ 
B)  $1 m n+4 m n^{2}+5 m^{2} n+10 m^{2} n^{2}$ 
C)  $10 \mathrm{~m}^{2} \mathrm{n}^{2}$ 
D)  $10 m^{2} n^{2}+5 m^{2} n+4 m n^{2}-9 m n$

Question 15

Find the missing monomial, factor or term.
-$8 x^{4} \cdot ?=32 x^{9}$

Accepted Answer

A)  $-x^{5}$ 
B)  $x^{5}$ 
C)  $4 x^{5}$ 
D)  $-4 x^{5}$ 
A)  $-x^{5}$ 
B)  $x^{5}$ 
C)  $4 x^{5}$ 
D)  $-4 x^{5}$

Question 16

Convert the given number to standard notation
-$2.41 \times 10^{-4}$

Accepted Answer

A)  0.000241 
B)  0.0000241 
C)  0.00241 
D)  - 241,000 
A)  0.000241 
B)  0.0000241 
C)  0.00241 
D)  - 241,000

Question 17

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

Accepted Answer

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

Question 18

Divide using synthetic division
-$\frac{x^{2}-11 x+24}{x-8}$

Accepted Answer

A)  $x+3$ 
B)  $x-4$ 
C)  $x+4$ 
D)  $x-3$ 
A)  $x+3$ 
B)  $x-4$ 
C)  $x+4$ 
D)  $x-3$

Question 19

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{4} y^{2}-5 x^{3} y^{3}-24 x^{2} y^{4}$

Accepted Answer

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

Question 20

$5 \mathrm{a} \cdot 3 \mathrm{a}^{2}$

Accepted Answer

A)  $5 a+3 a^{2}$ 
B)  $8 a^{3}$ 
C)  $15 a^{4}$ 
D)  $15 \mathrm{a}^{3}$ 
A)  $5 a+3 a^{2}$ 
B)  $8 a^{3}$ 
C)  $15 a^{4}$ 
D)  $15 \mathrm{a}^{3}$

Determine which factoring technique is appropriate for the given polynomial. - $x^{3}-8 x^{2}-7 x+56$

Find the GCF. -9, 18, 24

$\left(6 x^{8}-7 x^{6}+5 x^{2}+9\right)+\left(6 x^{7}+3 x^{6}-5 x\right)$

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

Factor the GCF out of the given expression. - $20 x^{8}+20 x$

Factor by grouping. - $x^{3}-x^{2}+10 x-10$

The national debt of a small country is $\$ 7,740,000,000$ and the population is $2,396,000$ . What is the amount of debt per person?

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4}-1$

Divide. Assume all variables are nonzero - $\left(16 \mathrm{x}^{3}+24 \mathrm{x}^{2}+12 \mathrm{x}\right) \div(4 \mathrm{x})$

$(4 \mathrm{x}+10)(\mathrm{x}-10)$

Determine which factoring technique is appropriate for the given polynomial. - $24 x^{2}-30 x+6$

$\left(8 x^{4}-4 x^{3}-9 x^{2}+2\right)-\left(2 x^{4}+6 x^{3}-6 x^{2}-5\right)$

Find the number of molecules in the given quantity of a compound whose molar mass is given. Express your answer in scientific notation, rounding the decimal part to the nearest hundredth. -50 grams of carbon monoxide (CO); molar mass: 28.01 grams

$\left(-4 m n+4 m n^{2}-2 m^{2} n^{2}\right)+\left(5 m^{2} n+12 m^{2} n^{2}-5 m n\right)$

Find the missing monomial, factor or term. - $8 x^{4} \cdot ?=32 x^{9}$

Convert the given number to standard notation - $2.41 \times 10^{-4}$

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

Divide using synthetic division - $\frac{x^{2}-11 x+24}{x-8}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4} y^{2}-5 x^{3} y^{3}-24 x^{2} y^{4}$

$5 \mathrm{a} \cdot 3 \mathrm{a}^{2}$

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. - x3−8x2−7x+56x^{3}-8 x^{2}-7 x+56x3−8x2−7x+56

Find the GCF. -9, 18, 24

(6x8−7x6+5x2+9)+(6x7+3x6−5x)\left(6 x^{8}-7 x^{6}+5 x^{2}+9\right)+\left(6 x^{7}+3 x^{6}-5 x\right)(6x8−7x6+5x2+9)+(6x7+3x6−5x)

Find the special product using the appropriate formula - f(x)=8x2,g(x)=3x3f(x)=8 x^{2}, g(x)=3 x^{3}f(x)=8x2,g(x)=3x3

Factor the GCF out of the given expression. - 20x8+20x20 x^{8}+20 x20x8+20x

Factor by grouping. - x3−x2+10x−10x^{3}-x^{2}+10 x-10x3−x2+10x−10

The national debt of a small country is $7,740,000,000\$ 7,740,000,000$7,740,000,000 and the population is 2,396,0002,396,0002,396,000 . What is the amount of debt per person?

Factor completely. If the polynomial cannot be factored, write "prime." - x4−1x^{4}-1x4−1

Divide. Assume all variables are nonzero - (16x3+24x2+12x)÷(4x)\left(16 \mathrm{x}^{3}+24 \mathrm{x}^{2}+12 \mathrm{x}\right) \div(4 \mathrm{x})(16x3+24x2+12x)÷(4x)

(4x+10)(x−10)(4 \mathrm{x}+10)(\mathrm{x}-10)(4x+10)(x−10)

Determine which factoring technique is appropriate for the given polynomial. - 24x2−30x+624 x^{2}-30 x+624x2−30x+6

(8x4−4x3−9x2+2)−(2x4+6x3−6x2−5)\left(8 x^{4}-4 x^{3}-9 x^{2}+2\right)-\left(2 x^{4}+6 x^{3}-6 x^{2}-5\right)(8x4−4x3−9x2+2)−(2x4+6x3−6x2−5)

Find the number of molecules in the given quantity of a compound whose molar mass is given. Express your answer in scientific notation, rounding the decimal part to the nearest hundredth. -50 grams of carbon monoxide (CO); molar mass: 28.01 grams

(−4mn+4mn2−2m2n2)+(5m2n+12m2n2−5mn)\left(-4 m n+4 m n^{2}-2 m^{2} n^{2}\right)+\left(5 m^{2} n+12 m^{2} n^{2}-5 m n\right)(−4mn+4mn2−2m2n2)+(5m2n+12m2n2−5mn)

Find the missing monomial, factor or term. - 8x4⋅?=32x98 x^{4} \cdot ?=32 x^{9}8x4⋅?=32x9

Convert the given number to standard notation - 2.41×10−42.41 \times 10^{-4}2.41×10−4

Factor completely. If the polynomial cannot be factored, write "prime." - 8x3+y38 x^{3}+y^{3}8x3+y3

Divide using synthetic division - x2−11x+24x−8\frac{x^{2}-11 x+24}{x-8}x−8x2−11x+24​

Factor completely. If the polynomial cannot be factored, write "prime." - x4y2−5x3y3−24x2y4x^{4} y^{2}-5 x^{3} y^{3}-24 x^{2} y^{4}x4y2−5x3y3−24x2y4

5a⋅3a25 \mathrm{a} \cdot 3 \mathrm{a}^{2}5a⋅3a2

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. - $x^{3}-8 x^{2}-7 x+56$

$\left(6 x^{8}-7 x^{6}+5 x^{2}+9\right)+\left(6 x^{7}+3 x^{6}-5 x\right)$

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

Factor the GCF out of the given expression. - $20 x^{8}+20 x$

Factor by grouping. - $x^{3}-x^{2}+10 x-10$

The national debt of a small country is $\$ 7,740,000,000$ and the population is $2,396,000$ . What is the amount of debt per person?

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4}-1$

Divide. Assume all variables are nonzero - $\left(16 \mathrm{x}^{3}+24 \mathrm{x}^{2}+12 \mathrm{x}\right) \div(4 \mathrm{x})$

$(4 \mathrm{x}+10)(\mathrm{x}-10)$

Determine which factoring technique is appropriate for the given polynomial. - $24 x^{2}-30 x+6$

$\left(8 x^{4}-4 x^{3}-9 x^{2}+2\right)-\left(2 x^{4}+6 x^{3}-6 x^{2}-5\right)$

$\left(-4 m n+4 m n^{2}-2 m^{2} n^{2}\right)+\left(5 m^{2} n+12 m^{2} n^{2}-5 m n\right)$

Find the missing monomial, factor or term. - $8 x^{4} \cdot ?=32 x^{9}$

Convert the given number to standard notation - $2.41 \times 10^{-4}$

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

Divide using synthetic division - $\frac{x^{2}-11 x+24}{x-8}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4} y^{2}-5 x^{3} y^{3}-24 x^{2} y^{4}$

$5 \mathrm{a} \cdot 3 \mathrm{a}^{2}$