Question 1

Find the missing dividend or divisor
-$\frac{?}{6 x}=3 x^{2}$

Accepted Answer

A)  $18 x$ 
B)  $18 x^{2}$ 
C)  $18 x^{4}$ 
D)  $18 x^{3}$ 
A)  $18 x$ 
B)  $18 x^{2}$ 
C)  $18 x^{4}$ 
D)  $18 x^{3}$

Question 2

A triangle is 6 centimeters wider than it is tall. The area is 140 square $\mathrm{cm}$. Find the width (length of the base).

Accepted Answer

A)  20 centimeters 
B)  6 centimeters 
C)  21 centimeters 
D)  14 centimeters 
A)  20 centimeters 
B)  6 centimeters 
C)  21 centimeters 
D)  14 centimeters

Question 3

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 x^{6}-x^{5}-4 x+1$

Accepted Answer

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

Question 4

Divide using long division.
-$\frac{3 x^{2}+17 x-10}{x+7}$

Accepted Answer

A)  $3 x+4+\frac{18}{x+7}$ 
B)  $3 x-4$ 
C)  $3 x-4-\frac{18}{x+7}$ 
D)  $3 x-4+\frac{18}{x+7}$ 
A)  $3 x+4+\frac{18}{x+7}$ 
B)  $3 x-4$ 
C)  $3 x-4-\frac{18}{x+7}$ 
D)  $3 x-4+\frac{18}{x+7}$

Question 5

Determine the coefficient and the degree of each term in the polynomial.
-$5 x^{4}+4 x+2$

Accepted Answer

A)  Coefficients: 4, 1, 0; degrees: $5,-4,-2$ 
B)  Coefficients: 5, - 4, - 2;Degrees: 4, 1, 0 
C)  Coefficients: 5, 4, 2; degrees: $4,1,0$ 
D)  Coefficients: 4, 1, 0; degrees: 5, 4, 2 
A)  Coefficients: 4, 1, 0; degrees: $5,-4,-2$ 
B)  Coefficients: 5, - 4, - 2;Degrees: 4, 1, 0 
C)  Coefficients: 5, 4, 2; degrees: $4,1,0$ 
D)  Coefficients: 4, 1, 0; degrees: 5, 4, 2

Question 6

Determine which factoring technique is appropriate for the given polynomial.
-$x^{2}-25$

Accepted Answer

A)  factor out GCF 
B)  difference of cubes 
C)  difference of squares 
D)  sum of squares 
A)  factor out GCF 
B)  difference of cubes 
C)  difference of squares 
D)  sum of squares

Question 7

The mass of an electron is approximately $9.11 \times 10^{-28}$ grams. Find the mass of $296,000,000$ electrons.

Accepted Answer

A)  $2.7 \times 10^{-18}$ grams 
B)  $2.7 \times 10^{-17}$ grams 
C)  $2.7 \times 10^{-19}$ grams 
D)  $2.7 \times 10^{-20}$ grams 
A)  $2.7 \times 10^{-18}$ grams 
B)  $2.7 \times 10^{-17}$ grams 
C)  $2.7 \times 10^{-19}$ grams 
D)  $2.7 \times 10^{-20}$ grams

Question 8

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

Accepted Answer

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

Question 9

Find the GCF.
-10s, 15

Accepted Answer

A)  10 
B)  $30 \mathrm{~s}$ 
C)  $5 \mathrm{~s}$ 
D)  5 
A)  10 
B)  $30 \mathrm{~s}$ 
C)  $5 \mathrm{~s}$ 
D)  5

Question 10

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2} y^{2}+6 x y-40$

Accepted Answer

A)  $(x y-10)(x y+4)$ 
B)  $(x y-10)(x y+1)$ 
C)  $(x y+10)(x y-4)$ 
D)  Prime 
A)  $(x y-10)(x y+4)$ 
B)  $(x y-10)(x y+1)$ 
C)  $(x y+10)(x y-4)$ 
D)  Prime

Question 11

Factor completely. If the polynomial cannot be factored, write "prime."
-$25 \mathrm{x}^{2}-80 \mathrm{x}+64$

Accepted Answer

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

Question 12

Factor the GCF out of the given expression.
-$8 m^{7}+16 m^{5}+40 m^{2}$

Accepted Answer

A)  $8 m\left(1 m^{7}+2 m^{5}+5 m^{2}\right)$ 
B)  $8\left(1 m^{7}+2 m^{5}+5 m^{2}\right)$ 
C)  $m^{2}\left(8 m^{5}+16 m^{3}+40\right)$ 
D)  $8 m^{2}\left(1 m^{5}+2 m^{3}+5\right)$ 
A)  $8 m\left(1 m^{7}+2 m^{5}+5 m^{2}\right)$ 
B)  $8\left(1 m^{7}+2 m^{5}+5 m^{2}\right)$ 
C)  $m^{2}\left(8 m^{5}+16 m^{3}+40\right)$ 
D)  $8 m^{2}\left(1 m^{5}+2 m^{3}+5\right)$

Question 13

Find the GCF.
-$15 \mathrm{~m}^{5}, 135 \mathrm{~m}^{7}$

Accepted Answer

A)  $15 \mathrm{~m}^{2}$ 
B)  $135 m^{5}$ 
C)  $2025 \mathrm{~m}^{2}$ 
D)  $15 m^{5}$ 
A)  $15 \mathrm{~m}^{2}$ 
B)  $135 m^{5}$ 
C)  $2025 \mathrm{~m}^{2}$ 
D)  $15 m^{5}$

Question 14

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

Accepted Answer

A)  $(c+6 d)\left(c^{2}-6 o d+36 d^{2}\right)$ 
B)  $(\mathrm{c}-6 \mathrm{~d})\left(\mathrm{c}^{2}+36 \mathrm{~d}^{2}\right)$ 
C)  $(c-6 d)\left(c^{2}+6 o d+36 d^{2}\right)$ 
D)  $\left(c+216 \mathrm{~d}^{3}\right)\left(\mathrm{c}^{2}-1\right)$ 
A)  $(c+6 d)\left(c^{2}-6 o d+36 d^{2}\right)$ 
B)  $(\mathrm{c}-6 \mathrm{~d})\left(\mathrm{c}^{2}+36 \mathrm{~d}^{2}\right)$ 
C)  $(c-6 d)\left(c^{2}+6 o d+36 d^{2}\right)$ 
D)  $\left(c+216 \mathrm{~d}^{3}\right)\left(\mathrm{c}^{2}-1\right)$

Question 15

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$\frac{5 x^{-6}}{y^{-2} z^{7}}$

Accepted Answer

A)  $\frac{y^{2}}{5 x^{6} z^{7}}$ 
B)  $\frac{5 y^{2}}{x^{6} z^{7}}$ 
C)  $\frac{5 x^{6}}{y^{2} z^{7}}$ 
D)  $\frac{5}{x^{6} y^{2} z^{7}}$ 
A)  $\frac{y^{2}}{5 x^{6} z^{7}}$ 
B)  $\frac{5 y^{2}}{x^{6} z^{7}}$ 
C)  $\frac{5 x^{6}}{y^{2} z^{7}}$ 
D)  $\frac{5}{x^{6} y^{2} z^{7}}$

Question 16

Factor the GCF out of the given expression.
-$5 x^{2}+15 x$

Accepted Answer

A)  $5 x(x+3)$ 
B)  $5 x(x+15)$ 
C)  $x(5 x+15)$ 
D)  $5 x^{2}(x+3)$ 
A)  $5 x(x+3)$ 
B)  $5 x(x+15)$ 
C)  $x(5 x+15)$ 
D)  $5 x^{2}(x+3)$

Question 17

Find the mass, in grams, for the given number of molecules of a compound whose molar mass is given. Round your answer to the nearest hundredth of a gram.
-$1.93 \times 10^{22}$ molecules of calcium nitrate $\left(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\right)$; molar mass 164.10 grams

Accepted Answer

A)  5.26 grams 
B)  1.18 grams 
C)  0.03 grams 
D)  316.71 grams 
A)  5.26 grams 
B)  1.18 grams 
C)  0.03 grams 
D)  316.71 grams

Question 18

Factor completely. If the polynomial cannot be factored, write "prime."
-$216 y^{3}-343$

Accepted Answer

A)  $(216 y-7)\left(y^{2}+42 y+49\right)$ 
B)  $(6 y+7)\left(36 y^{2}-42 y+49\right)$ 
C)  $(6 y-7)\left(36 y^{2}+49\right)$ 
D)  $(6 y-7)\left(36 y^{2}+42 y+49\right)$ 
A)  $(216 y-7)\left(y^{2}+42 y+49\right)$ 
B)  $(6 y+7)\left(36 y^{2}-42 y+49\right)$ 
C)  $(6 y-7)\left(36 y^{2}+49\right)$ 
D)  $(6 y-7)\left(36 y^{2}+42 y+49\right)$

Question 19

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 x^{4}+14 x^{3}-8 x^{2}$

Accepted Answer

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

Question 20

Find the missing factor or exponent(s).
-$\left(-3 a ? a^{3} ?\right)^{3}=-27 a^{18} b^{12}$

Accepted Answer

A)  4,6 
B)  6,4 
C)  9,7 
D)  7,9 
A)  4,6 
B)  6,4 
C)  9,7 
D)  7,9

Find the missing dividend or divisor - $\frac{?}{6 x}=3 x^{2}$

A triangle is 6 centimeters wider than it is tall. The area is 140 square $\mathrm{cm}$ . Find the width (length of the base). $A triangle is 6 centimeters wider than it is tall. The area is 140 square \mathrm{cm} . Find the width (length of the base).$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{6}-x^{5}-4 x+1$

Divide using long division. - $\frac{3 x^{2}+17 x-10}{x+7}$

Determine the coefficient and the degree of each term in the polynomial. - $5 x^{4}+4 x+2$

Determine which factoring technique is appropriate for the given polynomial. - $x^{2}-25$

The mass of an electron is approximately $9.11 \times 10^{-28}$ grams. Find the mass of $296,000,000$ electrons.

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

Find the GCF. -10s, 15

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2} y^{2}+6 x y-40$

Factor completely. If the polynomial cannot be factored, write "prime." - $25 \mathrm{x}^{2}-80 \mathrm{x}+64$

Factor the GCF out of the given expression. - $8 m^{7}+16 m^{5}+40 m^{2}$

Find the GCF. - $15 \mathrm{~m}^{5}, 135 \mathrm{~m}^{7}$

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

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{5 x^{-6}}{y^{-2} z^{7}}$

Factor the GCF out of the given expression. - $5 x^{2}+15 x$

Find the mass, in grams, for the given number of molecules of a compound whose molar mass is given. Round your answer to the nearest hundredth of a gram. - $1.93 \times 10^{22}$ molecules of calcium nitrate $\left(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\right)$ ; molar mass 164.10 grams

Factor completely. If the polynomial cannot be factored, write "prime." - $216 y^{3}-343$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{4}+14 x^{3}-8 x^{2}$

Find the missing factor or exponent(s). - $\left(-3 a ? a^{3} ?\right)^{3}=-27 a^{18} b^{12}$

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

Find the missing dividend or divisor - ?6x=3x2\frac{?}{6 x}=3 x^{2}6x?​=3x2

A triangle is 6 centimeters wider than it is tall. The area is 140 square cm\mathrm{cm}cm . Find the width (length of the base).

Factor completely. If the polynomial cannot be factored, write "prime." - 4x6−x5−4x+14 x^{6}-x^{5}-4 x+14x6−x5−4x+1

Divide using long division. - 3x2+17x−10x+7\frac{3 x^{2}+17 x-10}{x+7}x+73x2+17x−10​

Determine the coefficient and the degree of each term in the polynomial. - 5x4+4x+25 x^{4}+4 x+25x4+4x+2

Determine which factoring technique is appropriate for the given polynomial. - x2−25x^{2}-25x2−25

The mass of an electron is approximately 9.11×10−289.11 \times 10^{-28}9.11×10−28 grams. Find the mass of 296,000,000296,000,000296,000,000 electrons.

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

Find the GCF. -10s, 15

Factor completely. If the polynomial cannot be factored, write "prime." - x2y2+6xy−40x^{2} y^{2}+6 x y-40x2y2+6xy−40

Factor completely. If the polynomial cannot be factored, write "prime." - 25x2−80x+6425 \mathrm{x}^{2}-80 \mathrm{x}+6425x2−80x+64

Factor the GCF out of the given expression. - 8m7+16m5+40m28 m^{7}+16 m^{5}+40 m^{2}8m7+16m5+40m2

Find the GCF. - 15 m5,135 m715 \mathrm{~m}^{5}, 135 \mathrm{~m}^{7}15 m5,135 m7

Factor completely. If the polynomial cannot be factored, write "prime." - c3−216d3c^{3}-216 d^{3}c3−216d3

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - 5x−6y−2z7\frac{5 x^{-6}}{y^{-2} z^{7}}y−2z75x−6​

Factor the GCF out of the given expression. - 5x2+15x5 x^{2}+15 x5x2+15x

Factor completely. If the polynomial cannot be factored, write "prime." - 216y3−343216 y^{3}-343216y3−343

Factor completely. If the polynomial cannot be factored, write "prime." - 4x4+14x3−8x24 x^{4}+14 x^{3}-8 x^{2}4x4+14x3−8x2

Find the missing factor or exponent(s). - (−3a?a3?)3=−27a18b12\left(-3 a ? a^{3} ?\right)^{3}=-27 a^{18} b^{12}(−3a?a3?)3=−27a18b12

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

Find the missing dividend or divisor - $\frac{?}{6 x}=3 x^{2}$

A triangle is 6 centimeters wider than it is tall. The area is 140 square $\mathrm{cm}$ . Find the width (length of the base). $A triangle is 6 centimeters wider than it is tall. The area is 140 square \mathrm{cm} . Find the width (length of the base).$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{6}-x^{5}-4 x+1$

Divide using long division. - $\frac{3 x^{2}+17 x-10}{x+7}$

Determine the coefficient and the degree of each term in the polynomial. - $5 x^{4}+4 x+2$

Determine which factoring technique is appropriate for the given polynomial. - $x^{2}-25$

The mass of an electron is approximately $9.11 \times 10^{-28}$ grams. Find the mass of $296,000,000$ electrons.

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." - $x^{2} y^{2}+6 x y-40$

Factor completely. If the polynomial cannot be factored, write "prime." - $25 \mathrm{x}^{2}-80 \mathrm{x}+64$

Factor the GCF out of the given expression. - $8 m^{7}+16 m^{5}+40 m^{2}$

Find the GCF. - $15 \mathrm{~m}^{5}, 135 \mathrm{~m}^{7}$

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

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{5 x^{-6}}{y^{-2} z^{7}}$

Factor the GCF out of the given expression. - $5 x^{2}+15 x$

Factor completely. If the polynomial cannot be factored, write "prime." - $216 y^{3}-343$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{4}+14 x^{3}-8 x^{2}$

Find the missing factor or exponent(s). - $\left(-3 a ? a^{3} ?\right)^{3}=-27 a^{18} b^{12}$