Question 1

Determine whether the simplified version of the given expression would be a
-$(x-5)\left(x^{2}+5 x+25\right)$

Accepted Answer

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

Question 2

Evaluate the polynomial
-$x^{2}+3 y^{2}+2 x y$ for $x=5$ and $y=3$

Accepted Answer

A)  52 
B)  82 
C)  97 
D)  55 
A)  52 
B)  82 
C)  97 
D)  55

Question 3

Factor completely. If the polynomial cannot be factored, write "prime."
-$60 x^{6}+39 x^{4}+6 x^{2}$

Accepted Answer

A)  $\left(12 x^{3}+3\right)\left(5 x^{3}+2\right)$ 
B)  $3 x^{2}\left(5 x^{2}-2\right)\left(4 x^{2}-1\right)$ 
C)  $3\left(4 x^{4}+1\right)\left(5 x^{2}+2\right)$ 
D)  $3 x^{2}\left(4 x^{2}+1\right)\left(5 x^{2}+2\right)$ 
A)  $\left(12 x^{3}+3\right)\left(5 x^{3}+2\right)$ 
B)  $3 x^{2}\left(5 x^{2}-2\right)\left(4 x^{2}-1\right)$ 
C)  $3\left(4 x^{4}+1\right)\left(5 x^{2}+2\right)$ 
D)  $3 x^{2}\left(4 x^{2}+1\right)\left(5 x^{2}+2\right)$

Question 4

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{3}-1000$

Accepted Answer

A)  $(x-10)\left(x^{2}+100\right)$ 
B)  $(\mathrm{x}+10)\left(\mathrm{x}^{2}-10 \mathrm{x}+100\right)$ 
C)  $(x-10)\left(x^{2}+10 x+100\right)$ 
D)  $(x+1000)\left(x^{2}-1\right)$ 
A)  $(x-10)\left(x^{2}+100\right)$ 
B)  $(\mathrm{x}+10)\left(\mathrm{x}^{2}-10 \mathrm{x}+100\right)$ 
C)  $(x-10)\left(x^{2}+10 x+100\right)$ 
D)  $(x+1000)\left(x^{2}-1\right)$

Question 5

Factor the GCF out of the given expression.
-$9 x(x-4)+(x-4)$

Accepted Answer

A)  $(9 x-4)(x+1)$ 
B)  $(9 x+1)(x-4)$ 
C)  $9 x(x-4)$ 
D)  $(9 x+4)(x+1)$ 
A)  $(9 x-4)(x+1)$ 
B)  $(9 x+1)(x-4)$ 
C)  $9 x(x-4)$ 
D)  $(9 x+4)(x+1)$

Question 6

Find the missing monomial, factor or term.
-$(?)^{2}=x^{2}+16 x+64$

Accepted Answer

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

Question 7

Find the missing factor or exponent(s).
-$\left(\frac{x^{10} y^{7}}{z^{8}}\right)^{?}=\frac{x^{50} y^{35}}{z^{40}}$

Accepted Answer

A)  7 
B)  8 
C)  10 
D)  5 
A)  7 
B)  8 
C)  10 
D)  5

Question 8

$-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}$

Accepted Answer

A)  $-10 \mathrm{xz}^{7}$ 
B)  $-10 x ^6{z} ^7$ 
C)  $-10 x^{7} z^{6}$ 
D)  $-10 x z 6$ 
A)  $-10 \mathrm{xz}^{7}$ 
B)  $-10 x ^6{z} ^7$ 
C)  $-10 x^{7} z^{6}$ 
D)  $-10 x z 6$

Question 9

Factor completely. If the polynomial cannot be factored, write "prime."
-$16 x^{2}-8 x+1$

Accepted Answer

A)  $(4 x-1)^{2}$ 
B)  $(x+4)^{2}$ 
C)  $(4 x+1)^{2}$ 
D)  prime 
A)  $(4 x-1)^{2}$ 
B)  $(x+4)^{2}$ 
C)  $(4 x+1)^{2}$ 
D)  prime

Question 10

Factor completely. If the polynomial cannot be factored, write "prime."
-$2 x^{2}+2 x y-40 y^{2}$

Accepted Answer

A)  $(x-4 y)(2 x+10 y)$ 
B)  $2(x-4 y)(x+5 y)$ 
C)  $2(x+4 y)(x-5 y)$ 
D)  $(2 x+8 y)(x-5 y)$ 
A)  $(x-4 y)(2 x+10 y)$ 
B)  $2(x-4 y)(x+5 y)$ 
C)  $2(x+4 y)(x-5 y)$ 
D)  $(2 x+8 y)(x-5 y)$

Question 11

Factor completely. If the polynomial cannot be factored, write "prime."
-$3 x^{5}+9 x^{4} y-30 x^{3} y^{2}$

Accepted Answer

A)  $\left(3 x^{2}+6 x y\right)\left(x^{3}-5 y\right)$ 
B)  $(x-2 y)\left(3 x^{4}+15 x y\right)$ 
C)  $3 x^{3}(x+2 y)(x-5 y)$ 
D)  $3 x^{3}(x-2 y)(x+5 y)$ 
A)  $\left(3 x^{2}+6 x y\right)\left(x^{3}-5 y\right)$ 
B)  $(x-2 y)\left(3 x^{4}+15 x y\right)$ 
C)  $3 x^{3}(x+2 y)(x-5 y)$ 
D)  $3 x^{3}(x-2 y)(x+5 y)$

Question 12

Factor completely. If the polynomial cannot be factored, write "prime."
-$8 x^{3}-216 y^{3}$

Accepted Answer

A)  $8(x-3 y)\left(x^{2}+9 y^{2}\right)$ 
B)  $8(x-3 y)\left(x^{2}+3 x y+9 y^{2}\right)$ 
C)  $8(x+3 y)\left(x^{2}-3 x y+9 y^{2}\right)$ 
D)  $(8 x-3 y)\left(x^{2}+3 y+72 y^{2}\right)$ 
A)  $8(x-3 y)\left(x^{2}+9 y^{2}\right)$ 
B)  $8(x-3 y)\left(x^{2}+3 x y+9 y^{2}\right)$ 
C)  $8(x+3 y)\left(x^{2}-3 x y+9 y^{2}\right)$ 
D)  $(8 x-3 y)\left(x^{2}+3 y+72 y^{2}\right)$

Question 13

Divide using long division.
-$\frac{3 x^{2}+19 x+20}{x+4}$

Accepted Answer

A)  $3 x+7-\frac{8}{x+4}$ 
B)  $3 x+7+\frac{8}{x+4}$ 
C)  $3 x-7-\frac{8}{x+4}$ 
D)  $3 x+7$ 
A)  $3 x+7-\frac{8}{x+4}$ 
B)  $3 x+7+\frac{8}{x+4}$ 
C)  $3 x-7-\frac{8}{x+4}$ 
D)  $3 x+7$

Question 14

Convert the given number to scientific notation
-$1,054,000,000,000,000,000$

Accepted Answer

A)  $1.054 \times 10^{-18}$ 
B)  $1054 \times 10^{15}$ 
C)  $1.054 \times 10^{18}$ 
D)  $1054 \times 10^{-15}$ 
A)  $1.054 \times 10^{-18}$ 
B)  $1054 \times 10^{15}$ 
C)  $1.054 \times 10^{18}$ 
D)  $1054 \times 10^{-15}$

Question 15

Simplify. (A ssume all variables are nonzero.)
-$(13 \mathrm{x})^{0}$

Accepted Answer

A)  13 
B)  $13 x$ 
C)  0 
D)  1 
A)  13 
B)  $13 x$ 
C)  0 
D)  1

Question 16

Perform the indicated calculation. Express your answer using scientific notation.
-$\left(1.1 \times 10^{-5}\right)\left(1.5 \times 10^{-8}\right)$

Accepted Answer

A)  $1.65 \times 10^{13}$ 
B)  $1.65 \times 10^{-13}$ 
C)  $1.65 \times 10^{-3}$ 
D)  $2.6 \times 10^{13}$ 
A)  $1.65 \times 10^{13}$ 
B)  $1.65 \times 10^{-13}$ 
C)  $1.65 \times 10^{-3}$ 
D)  $2.6 \times 10^{13}$

Question 17

A rectangular garden has dimensions of 18 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 234 square feet?

Accepted Answer

A)  5.5 feet 
B)  5 feet 
C)  4 feet 
D)  3 feet 
A)  5.5 feet 
B)  5 feet 
C)  4 feet 
D)  3 feet

Question 18

Divide using long division.
-$\frac{x^{2}+7 x+7}{x+3}$

Accepted Answer

A)  $x+4+\frac{5}{x+3}$ 
B)  $\frac{x+4}{x+3}$ 
C)  $x+4-\frac{5}{x+3}$ 
D)  $x+5$ 
A)  $x+4+\frac{5}{x+3}$ 
B)  $\frac{x+4}{x+3}$ 
C)  $x+4-\frac{5}{x+3}$ 
D)  $x+5$

Question 19

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-16 x+64$

Accepted Answer

A)  $(x-4)^{2}$ 
B)  $(x+8)^{2}$ 
C)  $(x-8)^{2}$ 
D)  prime 
A)  $(x-4)^{2}$ 
B)  $(x+8)^{2}$ 
C)  $(x-8)^{2}$ 
D)  prime

Question 20

Factor completely. If the polynomial cannot be factored, write "prime."
-$15 x^{3}-2 x^{2}-8 x$

Accepted Answer

A)  $x(3 x+2)(5 x-4)$ 
B)  $(3 x-2)(5 x+4)$ 
C)  $x(15 x+1)(x-8)$ 
D)  $\left(x^{2}-4\right)(15 x+2)$ 
A)  $x(3 x+2)(5 x-4)$ 
B)  $(3 x-2)(5 x+4)$ 
C)  $x(15 x+1)(x-8)$ 
D)  $\left(x^{2}-4\right)(15 x+2)$

Determine whether the simplified version of the given expression would be a - $(x-5)\left(x^{2}+5 x+25\right)$

Evaluate the polynomial - $x^{2}+3 y^{2}+2 x y$ for $x=5$ and $y=3$

Factor completely. If the polynomial cannot be factored, write "prime." - $60 x^{6}+39 x^{4}+6 x^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-1000$

Factor the GCF out of the given expression. - $9 x(x-4)+(x-4)$

Find the missing monomial, factor or term. - $(?)^{2}=x^{2}+16 x+64$

Find the missing factor or exponent(s). - $\left(\frac{x^{10} y^{7}}{z^{8}}\right)^{?}=\frac{x^{50} y^{35}}{z^{40}}$

$-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $16 x^{2}-8 x+1$

Factor completely. If the polynomial cannot be factored, write "prime." - $2 x^{2}+2 x y-40 y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{5}+9 x^{4} y-30 x^{3} y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $8 x^{3}-216 y^{3}$

Divide using long division. - $\frac{3 x^{2}+19 x+20}{x+4}$

Convert the given number to scientific notation - $1,054,000,000,000,000,000$

Simplify. (A ssume all variables are nonzero.) - $(13 \mathrm{x})^{0}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(1.1 \times 10^{-5}\right)\left(1.5 \times 10^{-8}\right)$

A rectangular garden has dimensions of 18 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 234 square feet?

Divide using long division. - $\frac{x^{2}+7 x+7}{x+3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-16 x+64$

Factor completely. If the polynomial cannot be factored, write "prime." - $15 x^{3}-2 x^{2}-8 x$

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 whether the simplified version of the given expression would be a - (x−5)(x2+5x+25)(x-5)\left(x^{2}+5 x+25\right)(x−5)(x2+5x+25)

Evaluate the polynomial - x2+3y2+2xyx^{2}+3 y^{2}+2 x yx2+3y2+2xy for x=5x=5x=5 and y=3y=3y=3

Factor completely. If the polynomial cannot be factored, write "prime." - 60x6+39x4+6x260 x^{6}+39 x^{4}+6 x^{2}60x6+39x4+6x2

Factor completely. If the polynomial cannot be factored, write "prime." - x3−1000x^{3}-1000x3−1000

Factor the GCF out of the given expression. - 9x(x−4)+(x−4)9 x(x-4)+(x-4)9x(x−4)+(x−4)

Find the missing monomial, factor or term. - (?)2=x2+16x+64(?)^{2}=x^{2}+16 x+64(?)2=x2+16x+64

Find the missing factor or exponent(s). - (x10y7z8)?=x50y35z40\left(\frac{x^{10} y^{7}}{z^{8}}\right)^{?}=\frac{x^{50} y^{35}}{z^{40}}(z8x10y7​)?=z40x50y35​

−5x3z4⋅2x4z2-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}−5x3z4⋅2x4z2

Factor completely. If the polynomial cannot be factored, write "prime." - 16x2−8x+116 x^{2}-8 x+116x2−8x+1

Factor completely. If the polynomial cannot be factored, write "prime." - 2x2+2xy−40y22 x^{2}+2 x y-40 y^{2}2x2+2xy−40y2

Factor completely. If the polynomial cannot be factored, write "prime." - 3x5+9x4y−30x3y23 x^{5}+9 x^{4} y-30 x^{3} y^{2}3x5+9x4y−30x3y2

Factor completely. If the polynomial cannot be factored, write "prime." - 8x3−216y38 x^{3}-216 y^{3}8x3−216y3

Divide using long division. - 3x2+19x+20x+4\frac{3 x^{2}+19 x+20}{x+4}x+43x2+19x+20​

Convert the given number to scientific notation - 1,054,000,000,000,000,0001,054,000,000,000,000,0001,054,000,000,000,000,000

Simplify. (A ssume all variables are nonzero.) - (13x)0(13 \mathrm{x})^{0}(13x)0

Perform the indicated calculation. Express your answer using scientific notation. - (1.1×10−5)(1.5×10−8)\left(1.1 \times 10^{-5}\right)\left(1.5 \times 10^{-8}\right)(1.1×10−5)(1.5×10−8)

A rectangular garden has dimensions of 18 feet by 15 feet. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for 234 square feet?

Divide using long division. - x2+7x+7x+3\frac{x^{2}+7 x+7}{x+3}x+3x2+7x+7​

Factor completely. If the polynomial cannot be factored, write "prime." - x2−16x+64x^{2}-16 x+64x2−16x+64

Factor completely. If the polynomial cannot be factored, write "prime." - 15x3−2x2−8x15 x^{3}-2 x^{2}-8 x15x3−2x2−8x

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 whether the simplified version of the given expression would be a - $(x-5)\left(x^{2}+5 x+25\right)$

Evaluate the polynomial - $x^{2}+3 y^{2}+2 x y$ for $x=5$ and $y=3$

Factor completely. If the polynomial cannot be factored, write "prime." - $60 x^{6}+39 x^{4}+6 x^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{3}-1000$

Factor the GCF out of the given expression. - $9 x(x-4)+(x-4)$

Find the missing monomial, factor or term. - $(?)^{2}=x^{2}+16 x+64$

Find the missing factor or exponent(s). - $\left(\frac{x^{10} y^{7}}{z^{8}}\right)^{?}=\frac{x^{50} y^{35}}{z^{40}}$

$-5 x^{3} z^{4} \cdot 2 x^{4} z^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $16 x^{2}-8 x+1$

Factor completely. If the polynomial cannot be factored, write "prime." - $2 x^{2}+2 x y-40 y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $3 x^{5}+9 x^{4} y-30 x^{3} y^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $8 x^{3}-216 y^{3}$

Divide using long division. - $\frac{3 x^{2}+19 x+20}{x+4}$

Convert the given number to scientific notation - $1,054,000,000,000,000,000$

Simplify. (A ssume all variables are nonzero.) - $(13 \mathrm{x})^{0}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(1.1 \times 10^{-5}\right)\left(1.5 \times 10^{-8}\right)$

Divide using long division. - $\frac{x^{2}+7 x+7}{x+3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-16 x+64$

Factor completely. If the polynomial cannot be factored, write "prime." - $15 x^{3}-2 x^{2}-8 x$