Question 1

Find the missing factor or exponent(s).
-$\left(x^{7}\right)^{?} \cdot\left(x^{9}\right)^{3}=x^{62}$

Accepted Answer

A)  35 
B)  5 
C)  21 
D)  7 
A)  35 
B)  5 
C)  21 
D)  7

Question 2

Choose the one alternative that best completes the statement or answers thequestion.
-$a^{2} \cdot a^{3} \cdot a^{9}$

Accepted Answer

A)  a12 
B)  $a^{14}$ 
C)  $a^{5}$ 
D)  $\mathrm{a}^{15}$ 
A)  a12 
B)  $a^{14}$ 
C)  $a^{5}$ 
D)  $\mathrm{a}^{15}$

Question 3

Find the missing factor or exponent(s).
-$\left(\mathrm{x}^{?}\right)^{3}=\mathrm{x}^{39}$

Accepted Answer

A)  36 
B)  3 
C)  13 
D)  26 
A)  36 
B)  3 
C)  13 
D)  26

Question 4

Convert the given number to standard notation
-$4.3037 \times 10^{6}$

Accepted Answer

A)  430,370 
B)  $4,303,700$ 
C)  $43,037,000$ 
D)  258.222 
A)  430,370 
B)  $4,303,700$ 
C)  $43,037,000$ 
D)  258.222

Question 5

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

Accepted Answer

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

Question 6

Round your answer to the nearest whole number, if necessary.
-The distance an object moves in a straight line (in meters) is given by the function $\mathrm{f}(\mathrm{t})=9 \mathrm{t}^{2}-7 \mathrm{t}$, where $t$ is the time in seconds the object has been in motion. How far will an object move in 12 seconds?

Accepted Answer

A)  288 meters 
B)  900 meters 
C)  1212 meters 
D)  24 meters 
A)  288 meters 
B)  900 meters 
C)  1212 meters 
D)  24 meters

Question 7

Convert the given number to scientific notation
-$7,800,000$

Accepted Answer

A)  $7.8 \times 10^{-6}$ 
B)  $7.8 \times 10^{7}$ 
C)  $7.8 \times 10^{-7}$ 
D)  $7.8 \times 10^{6}$ 
A)  $7.8 \times 10^{-6}$ 
B)  $7.8 \times 10^{7}$ 
C)  $7.8 \times 10^{-7}$ 
D)  $7.8 \times 10^{6}$

Question 8

Find the GCF.
-16,20

Accepted Answer

A)  1 
B)  16 
C)  4 
D)  2 
A)  1 
B)  16 
C)  4 
D)  2

Question 9

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$-5 m^{-4}$

Accepted Answer

A)  $-\frac{1}{625 m^{4}}$ 
B)  $\frac{1}{625 m^{4}}$ 
C)  $-\frac{5}{m^{4}}$ 
D)  $\frac{625}{m^{4}}$ 
A)  $-\frac{1}{625 m^{4}}$ 
B)  $\frac{1}{625 m^{4}}$ 
C)  $-\frac{5}{m^{4}}$ 
D)  $\frac{625}{m^{4}}$

Question 10

Find the missing factor or exponent(s).
-$\left(\mathrm{x}^{3}\right)^{?}=\mathrm{x}^{27}$

Accepted Answer

A)  9 
B)  18 
C)  27 
D)  24 
A)  9 
B)  18 
C)  27 
D)  24

Question 11

Factor completely. If the polynomial cannot be factored, write "prime."
-$15 x^{4}-32 x^{3}+16 x^{2}$

Accepted Answer

A)  $x^{2}(15 x-1)(x-16)$ 
B)  $x^{2}(3 x-4)(5 x-4)$ 
C)  $x(3 x+4)(5 x+4)$ 
D)  $\left(15 x^{2}+4\right)\left(x^{2}+4\right)$ 
A)  $x^{2}(15 x-1)(x-16)$ 
B)  $x^{2}(3 x-4)(5 x-4)$ 
C)  $x(3 x+4)(5 x+4)$ 
D)  $\left(15 x^{2}+4\right)\left(x^{2}+4\right)$

Question 12

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\left(a^{-1}\right)^{-5}$

Accepted Answer

A)  $a^{5}$ 
B)  $a^{4}$ 
C)  $\frac{1}{a^{5}}$ 
D)  $\frac{1}{a^{4}}$ 
A)  $a^{5}$ 
B)  $a^{4}$ 
C)  $\frac{1}{a^{5}}$ 
D)  $\frac{1}{a^{4}}$

Question 13

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}+10 x+25$

Accepted Answer

A)  $(5 x-1)^{2}$ 
B)  $(x+5)^{2}$ 
C)  $(x-5)^{2}$ 
D)  prime 
A)  $(5 x-1)^{2}$ 
B)  $(x+5)^{2}$ 
C)  $(x-5)^{2}$ 
D)  prime

Question 14

Evaluate the polynomial or polynomial function for the given value of the variable.
-$f(x)=3 x^{3}-9 x^{2}-2 x+1, f(-1)$

Accepted Answer

A)  -7 
B)  -13 
C)  7 
D)  -9 
A)  -7 
B)  -13 
C)  7 
D)  -9

Question 15

Determine the coefficient and the degree of each term in the polynomial.
-$-3 x^{4}-15 x^{2}+5 x+4 x^{6}$

Accepted Answer

A)  Coefficients: 4, 2, 1, 6
degrees: -3, -15, 5, 4 
B)  Coefficients: - 3, - 15, - 5, - 4
degrees: 4, 2, 1, 6 
C)  Coefficients: - 3, - 15, 5, 4 
degrees: 4, 2, 0, 6 
D)  Coefficients: - 3, - 15, 5, 4 
degrees: 4, 2, 1, 6 
A)  Coefficients: 4, 2, 1, 6
degrees: -3, -15, 5, 4 
B)  Coefficients: - 3, - 15, - 5, - 4
degrees: 4, 2, 1, 6 
C)  Coefficients: - 3, - 15, 5, 4 
degrees: 4, 2, 0, 6 
D)  Coefficients: - 3, - 15, 5, 4 
degrees: 4, 2, 1, 6

Question 16

$\left(4 x^{2}+3 x-2\right)\left(x^{2}+2 x+4\right)$

Accepted Answer

A)  $4 x^{4}+8 x^{3}+22 x^{2}+8 x-8$ 
B)  $4 x^{4}+8 x^{3}+20 x^{2}+8 x-8$ 
C)  $4 x^{4}+11 x^{3}+20 x^{2}+8 x-8$ 
D)  $4 x^{4}+11 x^{3}+22 x^{2}+8 x-8$ 
A)  $4 x^{4}+8 x^{3}+22 x^{2}+8 x-8$ 
B)  $4 x^{4}+8 x^{3}+20 x^{2}+8 x-8$ 
C)  $4 x^{4}+11 x^{3}+20 x^{2}+8 x-8$ 
D)  $4 x^{4}+11 x^{3}+22 x^{2}+8 x-8$

Question 17

A rectangular space of 390 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 11 feet.

Accepted Answer

A)  14 feet 
B)  26 feet 
C)  17 feet 
D)  15 feet 
A)  14 feet 
B)  26 feet 
C)  17 feet 
D)  15 feet

Question 18

Divide using long division.
-$\frac{x^{2}-4 x-12}{x-6}$

Accepted Answer

A)  $x+2+\frac{6}{x-6}$ 
B)  $x+2$ 
C)  $x-2$ 
D)  $x^{2}+2$ 
A)  $x+2+\frac{6}{x-6}$ 
B)  $x+2$ 
C)  $x-2$ 
D)  $x^{2}+2$

Question 19

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

Accepted Answer

A)  $(y z+6)\left(z^{2}-6 z+36 y\right)$ 
B)  $y(z+6)\left(z^{2}+36\right)$ 
C)  $y(z-6)\left(z^{2}+6 z+36\right)$ 
D)  $y(z+6)\left(z^{2}-6 z+36\right)$ 
A)  $(y z+6)\left(z^{2}-6 z+36 y\right)$ 
B)  $y(z+6)\left(z^{2}+36\right)$ 
C)  $y(z-6)\left(z^{2}+6 z+36\right)$ 
D)  $y(z+6)\left(z^{2}-6 z+36\right)$

Question 20

The height of a triangle is 4 centimeters more than the base. If the area of the triangle is 126 square centimeters, find the base and height of the triangle.

Accepted Answer

A)  Base: 10 centimeters; Height: 14 centimeters 
B)  Base: 13 centimeters; Height: 19 centimeters 
C)  Base: 14 centimeters; Height: 18 centimeters 
D)  Base: 13 centimeters; Height: 17 centimeters 
A)  Base: 10 centimeters; Height: 14 centimeters 
B)  Base: 13 centimeters; Height: 19 centimeters 
C)  Base: 14 centimeters; Height: 18 centimeters 
D)  Base: 13 centimeters; Height: 17 centimeters

Find the missing factor or exponent(s). - $\left(x^{7}\right)^{?} \cdot\left(x^{9}\right)^{3}=x^{62}$

Choose the one alternative that best completes the statement or answers thequestion. - $a^{2} \cdot a^{3} \cdot a^{9}$

Find the missing factor or exponent(s). - $\left(\mathrm{x}^{?}\right)^{3}=\mathrm{x}^{39}$

Convert the given number to standard notation - $4.3037 \times 10^{6}$

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

Convert the given number to scientific notation - $7,800,000$

Find the GCF. -16,20

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $-5 m^{-4}$

Find the missing factor or exponent(s). - $\left(\mathrm{x}^{3}\right)^{?}=\mathrm{x}^{27}$

Factor completely. If the polynomial cannot be factored, write "prime." - $15 x^{4}-32 x^{3}+16 x^{2}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(a^{-1}\right)^{-5}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+10 x+25$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f(x)=3 x^{3}-9 x^{2}-2 x+1, f(-1)$

Determine the coefficient and the degree of each term in the polynomial. - $-3 x^{4}-15 x^{2}+5 x+4 x^{6}$

$\left(4 x^{2}+3 x-2\right)\left(x^{2}+2 x+4\right)$

A rectangular space of 390 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 11 feet.

Divide using long division. - $\frac{x^{2}-4 x-12}{x-6}$

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

The height of a triangle is 4 centimeters more than the base. If the area of the triangle is 126 square centimeters, find the base and height of the triangle.

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 factor or exponent(s). - (x7)?⋅(x9)3=x62\left(x^{7}\right)^{?} \cdot\left(x^{9}\right)^{3}=x^{62}(x7)?⋅(x9)3=x62

Choose the one alternative that best completes the statement or answers thequestion. - a2⋅a3⋅a9a^{2} \cdot a^{3} \cdot a^{9}a2⋅a3⋅a9

Find the missing factor or exponent(s). - (x?)3=x39\left(\mathrm{x}^{?}\right)^{3}=\mathrm{x}^{39}(x?)3=x39

Convert the given number to standard notation - 4.3037×1064.3037 \times 10^{6}4.3037×106

Factor completely. If the polynomial cannot be factored, write "prime." - x4+4x3+2x2+8xx^{4}+4 x^{3}+2 x^{2}+8 xx4+4x3+2x2+8x

Convert the given number to scientific notation - 7,800,0007,800,0007,800,000

Find the GCF. -16,20

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - −5m−4-5 m^{-4}−5m−4

Find the missing factor or exponent(s). - (x3)?=x27\left(\mathrm{x}^{3}\right)^{?}=\mathrm{x}^{27}(x3)?=x27

Factor completely. If the polynomial cannot be factored, write "prime." - 15x4−32x3+16x215 x^{4}-32 x^{3}+16 x^{2}15x4−32x3+16x2

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (a−1)−5\left(a^{-1}\right)^{-5}(a−1)−5

Factor completely. If the polynomial cannot be factored, write "prime." - x2+10x+25x^{2}+10 x+25x2+10x+25

Evaluate the polynomial or polynomial function for the given value of the variable. - f(x)=3x3−9x2−2x+1,f(−1)f(x)=3 x^{3}-9 x^{2}-2 x+1, f(-1)f(x)=3x3−9x2−2x+1,f(−1)

Determine the coefficient and the degree of each term in the polynomial. - −3x4−15x2+5x+4x6-3 x^{4}-15 x^{2}+5 x+4 x^{6}−3x4−15x2+5x+4x6

(4x2+3x−2)(x2+2x+4)\left(4 x^{2}+3 x-2\right)\left(x^{2}+2 x+4\right)(4x2+3x−2)(x2+2x+4)

A rectangular space of 390 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 11 feet.

Divide using long division. - x2−4x−12x−6\frac{x^{2}-4 x-12}{x-6}x−6x2−4x−12​

Factor completely. If the polynomial cannot be factored, write "prime." - yz3+216yy z^{3}+216 yyz3+216y

The height of a triangle is 4 centimeters more than the base. If the area of the triangle is 126 square centimeters, find the base and height of the triangle.

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 factor or exponent(s). - $\left(x^{7}\right)^{?} \cdot\left(x^{9}\right)^{3}=x^{62}$

Choose the one alternative that best completes the statement or answers thequestion. - $a^{2} \cdot a^{3} \cdot a^{9}$

Find the missing factor or exponent(s). - $\left(\mathrm{x}^{?}\right)^{3}=\mathrm{x}^{39}$

Convert the given number to standard notation - $4.3037 \times 10^{6}$

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

Convert the given number to scientific notation - $7,800,000$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $-5 m^{-4}$

Find the missing factor or exponent(s). - $\left(\mathrm{x}^{3}\right)^{?}=\mathrm{x}^{27}$

Factor completely. If the polynomial cannot be factored, write "prime." - $15 x^{4}-32 x^{3}+16 x^{2}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(a^{-1}\right)^{-5}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+10 x+25$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f(x)=3 x^{3}-9 x^{2}-2 x+1, f(-1)$

Determine the coefficient and the degree of each term in the polynomial. - $-3 x^{4}-15 x^{2}+5 x+4 x^{6}$

$\left(4 x^{2}+3 x-2\right)\left(x^{2}+2 x+4\right)$

Divide using long division. - $\frac{x^{2}-4 x-12}{x-6}$

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