Question 1

Evaluate the polynomial or polynomial function for the given value of the variable.
-$-2 x^{3}-5 x^{2}+42$ for $x=-2$

Accepted Answer

A)  38 
B)  28 
C)  68 
D)  26 
A)  38 
B)  28 
C)  68 
D)  26

Question 2

Factor by grouping.
-$4 x^{2}-16 x-24 x+96$

Accepted Answer

A)  $(x-4)(4 x-24)$ 
B)  $4(x+4)(x+6)$ 
C)  $(x-4)(x-6)$ 
D)  $4(x-4)(x-6)$ 
A)  $(x-4)(4 x-24)$ 
B)  $4(x+4)(x+6)$ 
C)  $(x-4)(x-6)$ 
D)  $4(x-4)(x-6)$

Question 3

Convert the given number to standard notation
-$1.010 \times 10^{4}$

Accepted Answer

A)  40.4 
B)  1010 
C)  10,100 
D)  101,000 
A)  40.4 
B)  1010 
C)  10,100 
D)  101,000

Question 4

Find the special product using the appropriate formula
-$(\mathrm{x}-10)^{2}$

Accepted Answer

A)  $100 x^{2}-20 x+100$ 
B)  $x+100$ 
C)  $x^{2}-20 x+100$ 
D)  $x^{2}+100$ 
A)  $100 x^{2}-20 x+100$ 
B)  $x+100$ 
C)  $x^{2}-20 x+100$ 
D)  $x^{2}+100$

Question 5

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial.
-$-5 x^{2}+3 x^{3}+7 x^{4}+4$

Accepted Answer

A)  $7 \mathrm{x}^{4}, 7,4$ 
B)  $-5 x^{2}, 5,2$ 
C)  $3 x^{3}, 3,3$ 
D)  $-5 x^{2},-5,2$ 
A)  $7 \mathrm{x}^{4}, 7,4$ 
B)  $-5 x^{2}, 5,2$ 
C)  $3 x^{3}, 3,3$ 
D)  $-5 x^{2},-5,2$

Question 6

Find the missing factor or exponent(s).
-$\left(x^{?} \cdot y^{?}\right)^{6}=x^{18} y^{5}$

Accepted Answer

A)  3,9 
B)  6,9 
C)  3, 6 
D)  12,48 
A)  3,9 
B)  6,9 
C)  3, 6 
D)  12,48

Question 7

$4 a^{4} b^{5} c \cdot 9 b c^{4} d^{2}$

Accepted Answer

A)  $36 a^{4} b^{4} c^{3} d^{2}$ 
B)  $36 a^{4} b^{5} c^{4} d^{2}$ 
C)  $13 a^{4} b^{6} c^{5} d^{2}$ 
D)  $36 a^{4} b^{6} c^{5} d^{2}$ 
A)  $36 a^{4} b^{4} c^{3} d^{2}$ 
B)  $36 a^{4} b^{5} c^{4} d^{2}$ 
C)  $13 a^{4} b^{6} c^{5} d^{2}$ 
D)  $36 a^{4} b^{6} c^{5} d^{2}$

Question 8

Factor the GCF out of the given expression.
-$36 m^{8}+27 m^{6}-27 m^{3}$

Accepted Answer

A)  $9 m^{3}\left(4 m^{5}+3 m^{3}-3\right)$ 
B)  $9 m\left(4 m^{8}+3 m^{6}-3 m^{3}\right)$ 
C)  $9\left(4 m^{8}+3 m^{6}-3 m^{3}\right)$ 
D)  $m^{3}\left(36 m^{5}+27 m^{3}-27\right)$ 
A)  $9 m^{3}\left(4 m^{5}+3 m^{3}-3\right)$ 
B)  $9 m\left(4 m^{8}+3 m^{6}-3 m^{3}\right)$ 
C)  $9\left(4 m^{8}+3 m^{6}-3 m^{3}\right)$ 
D)  $m^{3}\left(36 m^{5}+27 m^{3}-27\right)$

Question 9

If a ball is thrown upward from the ground with an initial velocity of 48 feet per second, its height after $t$ seconds is given by the function $h(t)=-16 t^{2}+48 t$. Find the number of seconds before the ball lands on the ground.

Accepted Answer

A)  24 seconds 
B)  3 seconds 
C)  1.5 seconds 
D)  32 seconds 
A)  24 seconds 
B)  3 seconds 
C)  1.5 seconds 
D)  32 seconds

Question 10

Factor completely. If the polynomial cannot be factored, write "prime."
-$64 y^{4}-81$

Accepted Answer

A)  $\left(64 y^{2}+1\right)\left(y^{2}-81\right)$ 
B)  $\left(8 y^{2}-9\right)^{2}$ 
C)  $\left(8 y^{2}+9\right)^{2}$ 
D)  $\left(8 y^{2}+9\right)\left(8 y^{2}-9\right)$ 
A)  $\left(64 y^{2}+1\right)\left(y^{2}-81\right)$ 
B)  $\left(8 y^{2}-9\right)^{2}$ 
C)  $\left(8 y^{2}+9\right)^{2}$ 
D)  $\left(8 y^{2}+9\right)\left(8 y^{2}-9\right)$

Question 11

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$\frac{x^{-7}}{y^{-8}}$

Accepted Answer

A)  $x y^{-15}$ 
B)  $\frac{y^{8}}{x^{7}}$ 
C)  $\frac{1}{x^{7} y^{8}}$ 
D)  $x^{7} y^{8}$ 
A)  $x y^{-15}$ 
B)  $\frac{y^{8}}{x^{7}}$ 
C)  $\frac{1}{x^{7} y^{8}}$ 
D)  $x^{7} y^{8}$

Question 12

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$y^{-6} \cdot y^{-5}$

Accepted Answer

A)  $\frac{1}{y^{11}}$ 
B)  $\frac{1}{y^{-11}}$ 
C)  $y^{11}$ 
D)  $\frac{1}{y^{1}}$ 
A)  $\frac{1}{y^{11}}$ 
B)  $\frac{1}{y^{-11}}$ 
C)  $y^{11}$ 
D)  $\frac{1}{y^{1}}$

Question 13

Convert the given number to scientific notation
-0.0000000557011

Accepted Answer

A)  $5.57011 \times 10^{-8}$ 
B)  $5.57011 \times 10^{-9}$ 
C)  $5.57011 \times 10^{8}$ 
D)  $5.57011 \times 10^{-7}$ 
A)  $5.57011 \times 10^{-8}$ 
B)  $5.57011 \times 10^{-9}$ 
C)  $5.57011 \times 10^{8}$ 
D)  $5.57011 \times 10^{-7}$

Question 14

Divide. Assume all variables are nonzero
-$\frac{x^{8} y^{3}}{x^{5} y^{8}}$

Accepted Answer

A)  $\frac{x^{5}}{y^{3}}$ 
B)  $\frac{x^{3}}{y^{5}}$ 
C)  $x^{3} y^{5}$ 
D)  $\frac{y^{5}}{x^{3}}$ 
A)  $\frac{x^{5}}{y^{3}}$ 
B)  $\frac{x^{3}}{y^{5}}$ 
C)  $x^{3} y^{5}$ 
D)  $\frac{y^{5}}{x^{3}}$

Question 15

The area of a circle with radius $r$ is given by the function $A(r)=\pi r^{2}$. Find the area of the base of a circular storage tank if the radius is 5 feet long. Use $\pi \approx 3.14$.

Accepted Answer

A)  15.7 square feet 
B)  31.4 square feet 
C)  78.5 square feet 
D)  75 square feet 
A)  15.7 square feet 
B)  31.4 square feet 
C)  78.5 square feet 
D)  75 square feet

Question 16

The sun radiates energy into space at the rate of $3.9 \times 10^{26}$ joules per second. How many joules are emitted in three weeks?

Accepted Answer

A)  $7.1 \times 10^{32}$ joules 
B)  $7.1 \times 10^{53}$ joules 
C)  $7.1 \times 10^{26}$ joules 
D)  $7.1 \times 10^{59}$ joules 
A)  $7.1 \times 10^{32}$ joules 
B)  $7.1 \times 10^{53}$ joules 
C)  $7.1 \times 10^{26}$ joules 
D)  $7.1 \times 10^{59}$ joules

Question 17

The length of a rectangular frame is 10 centimeters more than the width. The area inside the frame is 75 square centimeters. Find the width of the frame.

Accepted Answer

A)  5 centimeters 
B)  8 centimeters 
C)  15 centimeters 
D)  25 centimeters 
A)  5 centimeters 
B)  8 centimeters 
C)  15 centimeters 
D)  25 centimeters

Question 18

Identify the polynomial as a 
-$13 x+2$

Accepted Answer

A)  Binomial 
B)  Trinomial 
C)  Monomial 
A)  Binomial 
B)  Trinomial 
C)  Monomial

Question 19

List the degree of each term and the degree of the polynomial.
-$x^{8} y z-x^{10} y^{2}-2 x^{7} y^{2} z^{3}$

Accepted Answer

A)  10, 12, 12; polynomial: 10 
B)  8, 12, 12; polynomial: 12 
C)  8,12, 12; polynomial: 8 
D)  10, 12, 12; polynomial: 12 
A)  10, 12, 12; polynomial: 10 
B)  8, 12, 12; polynomial: 12 
C)  8,12, 12; polynomial: 8 
D)  10, 12, 12; polynomial: 12

Question 20

Perform the indicated calculation. Express your answer using scientific notation.
-$\left(15 \times 10^{-8}\right) \div\left(3 \times 10^{3}\right)$

Accepted Answer

A)  $10 \times 10^{-5}$ 
B)  $10 \times 10^{-11}$ 
C)  $5 \times 10^{-5}$ 
D)  $5 \times 10^{-11}$ 
A)  $10 \times 10^{-5}$ 
B)  $10 \times 10^{-11}$ 
C)  $5 \times 10^{-5}$ 
D)  $5 \times 10^{-11}$

Evaluate the polynomial or polynomial function for the given value of the variable. - $-2 x^{3}-5 x^{2}+42$ for $x=-2$

Factor by grouping. - $4 x^{2}-16 x-24 x+96$

Convert the given number to standard notation - $1.010 \times 10^{4}$

Find the special product using the appropriate formula - $(\mathrm{x}-10)^{2}$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $-5 x^{2}+3 x^{3}+7 x^{4}+4$

Find the missing factor or exponent(s). - $\left(x^{?} \cdot y^{?}\right)^{6}=x^{18} y^{5}$

$4 a^{4} b^{5} c \cdot 9 b c^{4} d^{2}$

Factor the GCF out of the given expression. - $36 m^{8}+27 m^{6}-27 m^{3}$

If a ball is thrown upward from the ground with an initial velocity of 48 feet per second, its height after $t$ seconds is given by the function $h(t)=-16 t^{2}+48 t$ . Find the number of seconds before the ball lands on the ground.

Factor completely. If the polynomial cannot be factored, write "prime." - $64 y^{4}-81$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{x^{-7}}{y^{-8}}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $y^{-6} \cdot y^{-5}$

Convert the given number to scientific notation -0.0000000557011

Divide. Assume all variables are nonzero - $\frac{x^{8} y^{3}}{x^{5} y^{8}}$

The area of a circle with radius $r$ is given by the function $A(r)=\pi r^{2}$ . Find the area of the base of a circular storage tank if the radius is 5 feet long. Use $\pi \approx 3.14$ .

The sun radiates energy into space at the rate of $3.9 \times 10^{26}$ joules per second. How many joules are emitted in three weeks?

The length of a rectangular frame is 10 centimeters more than the width. The area inside the frame is 75 square centimeters. Find the width of the frame.

Identify the polynomial as a - $13 x+2$

List the degree of each term and the degree of the polynomial. - $x^{8} y z-x^{10} y^{2}-2 x^{7} y^{2} z^{3}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(15 \times 10^{-8}\right) \div\left(3 \times 10^{3}\right)$

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

Evaluate the polynomial or polynomial function for the given value of the variable. - −2x3−5x2+42-2 x^{3}-5 x^{2}+42−2x3−5x2+42 for x=−2x=-2x=−2

Factor by grouping. - 4x2−16x−24x+964 x^{2}-16 x-24 x+964x2−16x−24x+96

Convert the given number to standard notation - 1.010×1041.010 \times 10^{4}1.010×104

Find the special product using the appropriate formula - (x−10)2(\mathrm{x}-10)^{2}(x−10)2

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - −5x2+3x3+7x4+4-5 x^{2}+3 x^{3}+7 x^{4}+4−5x2+3x3+7x4+4

Find the missing factor or exponent(s). - (x?⋅y?)6=x18y5\left(x^{?} \cdot y^{?}\right)^{6}=x^{18} y^{5}(x?⋅y?)6=x18y5

4a4b5c⋅9bc4d24 a^{4} b^{5} c \cdot 9 b c^{4} d^{2}4a4b5c⋅9bc4d2

Factor the GCF out of the given expression. - 36m8+27m6−27m336 m^{8}+27 m^{6}-27 m^{3}36m8+27m6−27m3

If a ball is thrown upward from the ground with an initial velocity of 48 feet per second, its height after ttt seconds is given by the function h(t)=−16t2+48th(t)=-16 t^{2}+48 th(t)=−16t2+48t . Find the number of seconds before the ball lands on the ground.

Factor completely. If the polynomial cannot be factored, write "prime." - 64y4−8164 y^{4}-8164y4−81

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - x−7y−8\frac{x^{-7}}{y^{-8}}y−8x−7​

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - y−6⋅y−5y^{-6} \cdot y^{-5}y−6⋅y−5

Convert the given number to scientific notation -0.0000000557011

Divide. Assume all variables are nonzero - x8y3x5y8\frac{x^{8} y^{3}}{x^{5} y^{8}}x5y8x8y3​

The area of a circle with radius rrr is given by the function A(r)=πr2A(r)=\pi r^{2}A(r)=πr2 . Find the area of the base of a circular storage tank if the radius is 5 feet long. Use π≈3.14\pi \approx 3.14π≈3.14 .

The sun radiates energy into space at the rate of 3.9×10263.9 \times 10^{26}3.9×1026 joules per second. How many joules are emitted in three weeks?

The length of a rectangular frame is 10 centimeters more than the width. The area inside the frame is 75 square centimeters. Find the width of the frame.

Identify the polynomial as a - 13x+213 x+213x+2

List the degree of each term and the degree of the polynomial. - x8yz−x10y2−2x7y2z3x^{8} y z-x^{10} y^{2}-2 x^{7} y^{2} z^{3}x8yz−x10y2−2x7y2z3

Perform the indicated calculation. Express your answer using scientific notation. - (15×10−8)÷(3×103)\left(15 \times 10^{-8}\right) \div\left(3 \times 10^{3}\right)(15×10−8)÷(3×103)

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

Evaluate the polynomial or polynomial function for the given value of the variable. - $-2 x^{3}-5 x^{2}+42$ for $x=-2$

Factor by grouping. - $4 x^{2}-16 x-24 x+96$

Convert the given number to standard notation - $1.010 \times 10^{4}$

Find the special product using the appropriate formula - $(\mathrm{x}-10)^{2}$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $-5 x^{2}+3 x^{3}+7 x^{4}+4$

Find the missing factor or exponent(s). - $\left(x^{?} \cdot y^{?}\right)^{6}=x^{18} y^{5}$

$4 a^{4} b^{5} c \cdot 9 b c^{4} d^{2}$

Factor the GCF out of the given expression. - $36 m^{8}+27 m^{6}-27 m^{3}$

If a ball is thrown upward from the ground with an initial velocity of 48 feet per second, its height after $t$ seconds is given by the function $h(t)=-16 t^{2}+48 t$ . Find the number of seconds before the ball lands on the ground.

Factor completely. If the polynomial cannot be factored, write "prime." - $64 y^{4}-81$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{x^{-7}}{y^{-8}}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $y^{-6} \cdot y^{-5}$

Divide. Assume all variables are nonzero - $\frac{x^{8} y^{3}}{x^{5} y^{8}}$

The area of a circle with radius $r$ is given by the function $A(r)=\pi r^{2}$ . Find the area of the base of a circular storage tank if the radius is 5 feet long. Use $\pi \approx 3.14$ .

The sun radiates energy into space at the rate of $3.9 \times 10^{26}$ joules per second. How many joules are emitted in three weeks?

Identify the polynomial as a - $13 x+2$

List the degree of each term and the degree of the polynomial. - $x^{8} y z-x^{10} y^{2}-2 x^{7} y^{2} z^{3}$

Perform the indicated calculation. Express your answer using scientific notation. - $\left(15 \times 10^{-8}\right) \div\left(3 \times 10^{3}\right)$