Question 1

Multiply. $( 2 y + 1 ) \left( 2 y ^ { 2 } + 3 y + 2 \right)$

Accepted Answer

A)  $4 y ^ { 3 } + 8 y ^ { 2 } + 7 y + 2$ 
B)  $4 y ^ { 3 } - 11 y ^ { 2 } + 7 y + 2$ 
C)  $4 y ^ { 3 } + 10 y ^ { 2 } + 7 y - 2$ 
D)  $4 y ^ { 3 } - 9 y ^ { 2 } + 7 y + 2$ 
E)  $4 y ^ { 3 } + 12 y ^ { 2 } - 7 y - 2$ 
A)  $4 y ^ { 3 } + 8 y ^ { 2 } + 7 y + 2$ 
B)  $4 y ^ { 3 } - 11 y ^ { 2 } + 7 y + 2$ 
C)  $4 y ^ { 3 } + 10 y ^ { 2 } + 7 y - 2$ 
D)  $4 y ^ { 3 } - 9 y ^ { 2 } + 7 y + 2$ 
E)  $4 y ^ { 3 } + 12 y ^ { 2 } - 7 y - 2$

Question 2

Factor the expression completely. $4 a ^ { 2 } b c + 8 a b c - 96 b c$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(4 a ^...

Question 3

The product of two positive consecutive even integers is 168. Find the integers. ( Hint: Let x= the smaller even integer and x+2= the larger even integer.)

Accepted Answer

A)  $14,16$ 
B)  $16,18$ 
C)  $12,14$ 
D)  $10,12$ 
E)  $8,10$ 
A)  $14,16$ 
B)  $16,18$ 
C)  $12,14$ 
D)  $10,12$ 
E)  $8,10$

Question 4

$5 x ^ { 2 } + 4 x - 3 = 0$ is written in _________ form.

Accepted Answer

The answer of \(5 x ^ { 2 } +...

Question 5

Solve the equation. $( m + 2 ) ( 7 m + 2 ) - 8 = 28 m$, m = __________ If there is more than one solution, separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(( m + 2...

Question 6

Factor the expression completely. If the expression is prime, so indicate. $18 x ^ { 2 } + 15 x - 12$

Accepted Answer

A)  $2 ( 2 x - 1 ) ( 2 x + 3 )$ 
B)  $3 ( 2 x + 1 ) ( 3 x - 4 )$ 
C)  $3 ( 2 x - 1 ) ( 3 x + 4 )$ 
D)  $2 ( 2 x + 1 ) ( 2 x - 3 )$ 
E)  prime 
A)  $2 ( 2 x - 1 ) ( 2 x + 3 )$ 
B)  $3 ( 2 x + 1 ) ( 3 x - 4 )$ 
C)  $3 ( 2 x - 1 ) ( 3 x + 4 )$ 
D)  $2 ( 2 x + 1 ) ( 2 x - 3 )$ 
E)  prime

Question 7

Solve the equation by first clearing it of fractions. $\frac { 7 } { 2 } a ^ { 2 } = \frac { 5 } { 2 } - a$

Accepted Answer

A)  $a = 1 , a = - \frac { 5 } { 7 }$ 
B)  $a = 3 , a = \frac { 5 } { 7 }$ 
C)  $a = - 1 , a = \frac { 5 } { 7 }$ 
D)  $a = 2 , a = \frac { 5 } { 7 }$ 
E)  $a = 0 , a = - \frac { 5 } { 7 }$ 
A)  $a = 1 , a = - \frac { 5 } { 7 }$ 
B)  $a = 3 , a = \frac { 5 } { 7 }$ 
C)  $a = - 1 , a = \frac { 5 } { 7 }$ 
D)  $a = 2 , a = \frac { 5 } { 7 }$ 
E)  $a = 0 , a = - \frac { 5 } { 7 }$

Question 8

A __________ is the sum of one or more algebraic terms whose variables have whole-number exponents.

Accepted Answer

The answer of A __________ is the sum of one...

Question 9

Simplify the expression. Write the answer using positive exponents. $\left( \frac { 3 a ^ { 2 } b } { a ^ { - 5 } b ^ { 4 } } \right) ^ { 3 }$

Accepted Answer

The answer of Simplify the expression. Write the answer using...

Question 10

Simplify the expression. $\left( x ^ { 3 } \right) ^ { 7 }$

Accepted Answer

A)  $x ^ { 10 }$ 
B)  $\frac { 1 } { x ^ { 10 } }$ 
C)  $x ^ { 4 }$ 
D)  $\frac { 1 } { x ^ { 21 } }$ 
E)  $x ^ { 21 }$ 
A)  $x ^ { 10 }$ 
B)  $\frac { 1 } { x ^ { 10 } }$ 
C)  $x ^ { 4 }$ 
D)  $\frac { 1 } { x ^ { 21 } }$ 
E)  $x ^ { 21 }$

Question 11

Divide. Give the answer in scientific notation. $\frac { 6.3 \times 10 ^ { 3 } } { 3.5 \times 10 ^ { - 5 } }$

Accepted Answer

A)  $1.8 \times 10 ^ { 8 }$ 
B)  $1.8 \times 10 ^ { - 2 }$ 
C)  $1.8 \times 10 ^ { 2 }$ 
D)  $1.8 \times 10 ^ { - 8 }$ 
A)  $1.8 \times 10 ^ { 8 }$ 
B)  $1.8 \times 10 ^ { - 2 }$ 
C)  $1.8 \times 10 ^ { 2 }$ 
D)  $1.8 \times 10 ^ { - 8 }$

Question 12

Perform the indicated operation. $\left( \frac { 1 } { 2 } y ^ { 6 } - \frac { 1 } { 15 } y ^ { 4 } - \frac { 3 } { 2 } y ^ { 2 } \right) + \left( - \frac { 1 } { 4 } y ^ { 6 } - \frac { 1 } { 5 } y ^ { 4 } + \frac { 3 } { 4 } y ^ { 2 } \right)$

Accepted Answer

The answer of Perform the indicated operation. \(\left( \frac {...

Question 13

A __________ is a polynomial with one term. A __________ is a polynomial with two terms. A __________ is a polynomial with three terms.

Accepted Answer

The answer of A __________ is a polynomial with one...

Question 14

Perform the indicated operation. $\begin{array} { r } 
3 x ^ { 3 } - 3 x ^ { 2 } + 4 x - 3 \
- 2 x ^ { 3 } + 2 x ^ { 2 } + 2 x - 2 \
+ \quad 4 x ^ { 3 } - 6 x ^ { 2 } + 5 x - 10 \
\hline
\end{array}$

Accepted Answer

A)  $5 x ^ { 3 } - 7 x ^ { 2 } + 11 x - 15$ 
B)  $5 x ^ { 3 } - 7 x ^ { 2 } - 11 x + 15$ 
C)  $5 x ^ { 3 } - 7 x ^ { 2 } + 11 x + 15$ 
D)  $5 x ^ { 3 } + 7 x ^ { 2 } + 11 x - 15$ 
E)  $5 x ^ { 3 } - 7 x ^ { 2 } - 11 x - 15$ 
A)  $5 x ^ { 3 } - 7 x ^ { 2 } + 11 x - 15$ 
B)  $5 x ^ { 3 } - 7 x ^ { 2 } - 11 x + 15$ 
C)  $5 x ^ { 3 } - 7 x ^ { 2 } + 11 x + 15$ 
D)  $5 x ^ { 3 } + 7 x ^ { 2 } + 11 x - 15$ 
E)  $5 x ^ { 3 } - 7 x ^ { 2 } - 11 x - 15$

Question 15

Factor the expression completely. If the expression is prime, so indicate. $16 x ^ { 2 } y ^ { 2 } + 8 x y ^ { 2 } + y ^ { 2 }$

Accepted Answer

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

Question 16

Solve the equation. $2 y ^ { 2 } - 11 y + 5 = 0$, y = __________ If there is more than one solution separate your answers with commas.

Accepted Answer

The answer of Solve the equation. \(2 y ^ {...

Question 17

Each factor of a completely factored expression will be _________.

Accepted Answer

The answer of Each factor of a completely factored expression...

Question 18

Simplify the expression. $\left( \frac { 2 a ^ { 3 } b ^ { 2 } z ^ { - 5 } } { 3 a ^ { - 4 } b ^ { - 2 } z ^ { 5 } } \right) ^ { - 3 }$

Accepted Answer

A)  $\frac { 8 a ^ { 21 } b ^ { 12 } } { 27 z ^ { 30 } }$ 
B)  $\frac { 27 a ^ { 30 } } { 8 z ^ { 21 } b ^ { 12 } }$ 
C)  $\frac { 2 z ^ { 30 } } { 3 a ^ { 21 } b ^ { 12 } }$ 
D)  $\frac { 27 b ^ { 30 } } { 8 a ^ { 21 } z ^ { 12 } }$ 
E)  $\frac { 27 z ^ { 30 } } { 8 a ^ { 21 } b ^ { 12 } }$ 
A)  $\frac { 8 a ^ { 21 } b ^ { 12 } } { 27 z ^ { 30 } }$ 
B)  $\frac { 27 a ^ { 30 } } { 8 z ^ { 21 } b ^ { 12 } }$ 
C)  $\frac { 2 z ^ { 30 } } { 3 a ^ { 21 } b ^ { 12 } }$ 
D)  $\frac { 27 b ^ { 30 } } { 8 a ^ { 21 } z ^ { 12 } }$ 
E)  $\frac { 27 z ^ { 30 } } { 8 a ^ { 21 } b ^ { 12 } }$

Question 19

Factor the expression completely. $- 13 m ^ { 2 } + m ^ { 4 } + 36$ If the expression is prime, so indicate.

Accepted Answer

The answer of Factor the expression completely. \(- 13 m...

Question 20

Factor completely: $x ^ { 2 } - 4 x + 4 - 25 y ^ { 2 }$

Accepted Answer

The answer of Factor completely: \(x ^ { 2 }...

Multiply. $( 2 y + 1 ) \left( 2 y ^ { 2 } + 3 y + 2 \right)$

Factor the expression completely. $4 a ^ { 2 } b c + 8 a b c - 96 b c$ If the expression is prime, so indicate.

The product of two positive consecutive even integers is 168. Find the integers. ( Hint: Let x= the smaller even integer and x+2= the larger even integer.)

$5 x ^ { 2 } + 4 x - 3 = 0$ is written in _________ form.

Solve the equation. $( m + 2 ) ( 7 m + 2 ) - 8 = 28 m$ , m = __________ If there is more than one solution, separate your answers with commas.

Factor the expression completely. If the expression is prime, so indicate. $18 x ^ { 2 } + 15 x - 12$

Solve the equation by first clearing it of fractions. $\frac { 7 } { 2 } a ^ { 2 } = \frac { 5 } { 2 } - a$

A __________ is the sum of one or more algebraic terms whose variables have whole-number exponents.

Simplify the expression. Write the answer using positive exponents. $\left( \frac { 3 a ^ { 2 } b } { a ^ { - 5 } b ^ { 4 } } \right) ^ { 3 }$

Simplify the expression. $\left( x ^ { 3 } \right) ^ { 7 }$

Divide. Give the answer in scientific notation. $\frac { 6.3 \times 10 ^ { 3 } } { 3.5 \times 10 ^ { - 5 } }$

Perform the indicated operation. $\left( \frac { 1 } { 2 } y ^ { 6 } - \frac { 1 } { 15 } y ^ { 4 } - \frac { 3 } { 2 } y ^ { 2 } \right) + \left( - \frac { 1 } { 4 } y ^ { 6 } - \frac { 1 } { 5 } y ^ { 4 } + \frac { 3 } { 4 } y ^ { 2 } \right)$

A is a polynomial with one term. A is a polynomial with two terms. A __ is a polynomial with three terms.

Perform the indicated operation. 3-3+4x-3 -2+2+2x-2 +4-6+5x-10

Factor the expression completely. If the expression is prime, so indicate. $16 x ^ { 2 } y ^ { 2 } + 8 x y ^ { 2 } + y ^ { 2 }$

Solve the equation. $2 y ^ { 2 } - 11 y + 5 = 0$ , y = __________ If there is more than one solution separate your answers with commas.

Each factor of a completely factored expression will be _________.

Simplify the expression. $\left( \frac { 2 a ^ { 3 } b ^ { 2 } z ^ { - 5 } } { 3 a ^ { - 4 } b ^ { - 2 } z ^ { 5 } } \right) ^ { - 3 }$

Factor the expression completely. $- 13 m ^ { 2 } + m ^ { 4 } + 36$ If the expression is prime, so indicate.

Factor completely: $x ^ { 2 } - 4 x + 4 - 25 y ^ { 2 }$

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

Multiply. (2y+1)(2y2+3y+2)( 2 y + 1 ) \left( 2 y ^ { 2 } + 3 y + 2 \right)(2y+1)(2y2+3y+2)

Factor the expression completely. 4a2bc+8abc−96bc4 a ^ { 2 } b c + 8 a b c - 96 b c4a2bc+8abc−96bc If the expression is prime, so indicate.

The product of two positive consecutive even integers is 168. Find the integers. ( Hint: Let x= the smaller even integer and x+2= the larger even integer.)

5x2+4x−3=05 x ^ { 2 } + 4 x - 3 = 05x2+4x−3=0 is written in _________ form.

Solve the equation. (m+2)(7m+2)−8=28m( m + 2 ) ( 7 m + 2 ) - 8 = 28 m(m+2)(7m+2)−8=28m , m = __________ If there is more than one solution, separate your answers with commas.

Factor the expression completely. If the expression is prime, so indicate. 18x2+15x−1218 x ^ { 2 } + 15 x - 1218x2+15x−12

Solve the equation by first clearing it of fractions. 72a2=52−a\frac { 7 } { 2 } a ^ { 2 } = \frac { 5 } { 2 } - a27​a2=25​−a

A __________ is the sum of one or more algebraic terms whose variables have whole-number exponents.

Simplify the expression. Write the answer using positive exponents. (3a2ba−5b4)3\left( \frac { 3 a ^ { 2 } b } { a ^ { - 5 } b ^ { 4 } } \right) ^ { 3 }(a−5b43a2b​)3

Simplify the expression. (x3)7\left( x ^ { 3 } \right) ^ { 7 }(x3)7

Divide. Give the answer in scientific notation. 6.3×1033.5×10−5\frac { 6.3 \times 10 ^ { 3 } } { 3.5 \times 10 ^ { - 5 } }3.5×10−56.3×103​

A __________ is a polynomial with one term. A __________ is a polynomial with two terms. A __________ is a polynomial with three terms.

Perform the indicated operation. 3-3+4x-3 -2+2+2x-2 +4-6+5x-10

Factor the expression completely. If the expression is prime, so indicate. 16x2y2+8xy2+y216 x ^ { 2 } y ^ { 2 } + 8 x y ^ { 2 } + y ^ { 2 }16x2y2+8xy2+y2

Solve the equation. 2y2−11y+5=02 y ^ { 2 } - 11 y + 5 = 02y2−11y+5=0 , y = __________ If there is more than one solution separate your answers with commas.

Each factor of a completely factored expression will be _________.

Simplify the expression. (2a3b2z−53a−4b−2z5)−3\left( \frac { 2 a ^ { 3 } b ^ { 2 } z ^ { - 5 } } { 3 a ^ { - 4 } b ^ { - 2 } z ^ { 5 } } \right) ^ { - 3 }(3a−4b−2z52a3b2z−5​)−3

Factor the expression completely. −13m2+m4+36- 13 m ^ { 2 } + m ^ { 4 } + 36−13m2+m4+36 If the expression is prime, so indicate.

Factor completely: x2−4x+4−25y2x ^ { 2 } - 4 x + 4 - 25 y ^ { 2 }x2−4x+4−25y2

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Multiply. $( 2 y + 1 ) \left( 2 y ^ { 2 } + 3 y + 2 \right)$

Factor the expression completely. $4 a ^ { 2 } b c + 8 a b c - 96 b c$ If the expression is prime, so indicate.

$5 x ^ { 2 } + 4 x - 3 = 0$ is written in _________ form.

Solve the equation. $( m + 2 ) ( 7 m + 2 ) - 8 = 28 m$ , m = __________ If there is more than one solution, separate your answers with commas.

Factor the expression completely. If the expression is prime, so indicate. $18 x ^ { 2 } + 15 x - 12$

Solve the equation by first clearing it of fractions. $\frac { 7 } { 2 } a ^ { 2 } = \frac { 5 } { 2 } - a$

Simplify the expression. Write the answer using positive exponents. $\left( \frac { 3 a ^ { 2 } b } { a ^ { - 5 } b ^ { 4 } } \right) ^ { 3 }$

Simplify the expression. $\left( x ^ { 3 } \right) ^ { 7 }$

Divide. Give the answer in scientific notation. $\frac { 6.3 \times 10 ^ { 3 } } { 3.5 \times 10 ^ { - 5 } }$

A is a polynomial with one term. A is a polynomial with two terms. A __ is a polynomial with three terms.

Factor the expression completely. If the expression is prime, so indicate. $16 x ^ { 2 } y ^ { 2 } + 8 x y ^ { 2 } + y ^ { 2 }$

Solve the equation. $2 y ^ { 2 } - 11 y + 5 = 0$ , y = __________ If there is more than one solution separate your answers with commas.

Simplify the expression. $\left( \frac { 2 a ^ { 3 } b ^ { 2 } z ^ { - 5 } } { 3 a ^ { - 4 } b ^ { - 2 } z ^ { 5 } } \right) ^ { - 3 }$

Factor the expression completely. $- 13 m ^ { 2 } + m ^ { 4 } + 36$ If the expression is prime, so indicate.

Factor completely: $x ^ { 2 } - 4 x + 4 - 25 y ^ { 2 }$