Question 1

Perform the indicated operations and simplify. $2 \left( 4 t ^ { 2 } + 7 \right) - 8 \left( t ^ { 2 } + 7 \right) + 6 \left( 6 t ^ { 2 } + 7 \right)$

Accepted Answer

A)  $36 t ^ { 2 } - 84$ 
B)  $36 t ^ { 2 }$ 
C)  $52 t ^ { 2 } + 28$ 
D)  $- 36 t ^ { 2 } - 84$ 
E)  $52 t ^ { 2 } + 112$ 
A)  $36 t ^ { 2 } - 84$ 
B)  $36 t ^ { 2 }$ 
C)  $52 t ^ { 2 } + 28$ 
D)  $- 36 t ^ { 2 } - 84$ 
E)  $52 t ^ { 2 } + 112$

Question 2

Factor the difference of two squares. $v ^ { 2 } - \frac { 81 } { 4 }$

Accepted Answer

A)  $\left( v + \frac { 9 } { 2 } \right) ^ { 2 }$ 
B)  $\left( v - \frac { 9 } { 2 } \right) ^ { 2 }$ 
C)  $\left( v + \frac { 2 } { 9 } \right) ^ { 2 }$ 
D)  $\left( v + \frac { 9 } { 2 } \right) \left( v - \frac { 9 } { 2 } \right)$ 
E)  $\left( v + \frac { 2 } { 9 } \right) \left( v - \frac { 2 } { 9 } \right)$ 
A)  $\left( v + \frac { 9 } { 2 } \right) ^ { 2 }$ 
B)  $\left( v - \frac { 9 } { 2 } \right) ^ { 2 }$ 
C)  $\left( v + \frac { 2 } { 9 } \right) ^ { 2 }$ 
D)  $\left( v + \frac { 9 } { 2 } \right) \left( v - \frac { 9 } { 2 } \right)$ 
E)  $\left( v + \frac { 2 } { 9 } \right) \left( v - \frac { 2 } { 9 } \right)$

Question 3

Rewrite the expression $\frac { 1 } { 2 z ^ { - 5 } }$ using only positive exponents. Assume that z is not zero.

Accepted Answer

A)  $32 z ^ { 5 }$ 
B)  $- \frac { z ^ { 5 } } { 2 }$ 
C)  $\frac { z ^ { 5 } } { 2 }$ 
D)  $2 z ^ { 5 }$ 
E)  - $2 z ^ { 5 }$ 
A)  $32 z ^ { 5 }$ 
B)  $- \frac { z ^ { 5 } } { 2 }$ 
C)  $\frac { z ^ { 5 } } { 2 }$ 
D)  $2 z ^ { 5 }$ 
E)  - $2 z ^ { 5 }$

Question 4

Factor the trinomial, if possible. $10 y ^ { 2 } - 29 y - 72$

Accepted Answer

A)  $( 2 y - 9 ) ( 5 y + 8 )$ 
B)  $( 2 y + 9 ) ( 5 y + 8 )$ 
C)  $( 2 y - 9 ) ( 5 y - 8 )$ 
D)  $( 9 y + 2 ) ( 8 y - 5 )$ 
E) The trinomial is prime. 
A)  $( 2 y - 9 ) ( 5 y + 8 )$ 
B)  $( 2 y + 9 ) ( 5 y + 8 )$ 
C)  $( 2 y - 9 ) ( 5 y - 8 )$ 
D)  $( 9 y + 2 ) ( 8 y - 5 )$ 
E) The trinomial is prime.

Question 5

Find the value of $( - 2 ) ^ { - 5 }$ .

Accepted Answer

A)  $\frac { 1 } { 32 }$ 
B)  -10 
C)  10 
D)  $7,5$ 
E)  - $\frac { 1 } { 32 }$ 
A)  $\frac { 1 } { 32 }$ 
B)  -10 
C)  10 
D)  $7,5$ 
E)  - $\frac { 1 } { 32 }$

Question 6

A closed rectangular box has dimensions of length n inches, width n-4 inches, and height n+2 inches. Write a polynomial function $V ( n )$ that represents the volume of the box.

Accepted Answer

A)  $V ( n ) = n ^ { 3 } + 2 n ^ { 2 } - 8$ 
B)  $V ( n ) = n ^ { 3 } + 2 n ^ { 2 } - 8 n$ 
C)  $V ( n ) = n ^ { 3 } - 2 n ^ { 2 } - 8 n$ 
D)  $V ( n ) = n ^ { 3 } - 4 n ^ { 2 } - 8 n$ 
E)  $V ( n ) = n ^ { 3 } + 6 n ^ { 2 } - 8 n$ 
A)  $V ( n ) = n ^ { 3 } + 2 n ^ { 2 } - 8$ 
B)  $V ( n ) = n ^ { 3 } + 2 n ^ { 2 } - 8 n$ 
C)  $V ( n ) = n ^ { 3 } - 2 n ^ { 2 } - 8 n$ 
D)  $V ( n ) = n ^ { 3 } - 4 n ^ { 2 } - 8 n$ 
E)  $V ( n ) = n ^ { 3 } + 6 n ^ { 2 } - 8 n$

Question 7

Factor the perfect square trinomial $4 m ^ { 3 } - 72 m ^ { 2 } + 324 m$ .

Accepted Answer

A)  $4 m ( m + 9 ) ^ { 2 }$ 
B)  $4 ( m + 9 ) ^ { 3 }$ 
C)  $4 m ( m - 9 ) ^ { 2 }$ 
D)  $4 ( m - 9 ) ^ { 3 }$ 
E)  $4 m \left( m ^ { 2 } - 9 \right)$ 
A)  $4 m ( m + 9 ) ^ { 2 }$ 
B)  $4 ( m + 9 ) ^ { 3 }$ 
C)  $4 m ( m - 9 ) ^ { 2 }$ 
D)  $4 ( m - 9 ) ^ { 3 }$ 
E)  $4 m \left( m ^ { 2 } - 9 \right)$

Question 8

Use the rules of exponents to simplify the expression $\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$ using only positive exponents. Assume that neither x nor y is 0.

Accepted Answer

A)  $2 x ^ { 2 } y ^ { 4 }$ 
B)  $\frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }$ 
C)  $\frac { 1 } { 2 x ^ { 8 } y ^ { 12 } }$ 
D)  $4 x ^ { 2 } y ^ { 4 }$ 
E)  $\frac { 2 } { x ^ { 8 } y ^ { 12 } }$ 
A)  $2 x ^ { 2 } y ^ { 4 }$ 
B)  $\frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }$ 
C)  $\frac { 1 } { 2 x ^ { 8 } y ^ { 12 } }$ 
D)  $4 x ^ { 2 } y ^ { 4 }$ 
E)  $\frac { 2 } { x ^ { 8 } y ^ { 12 } }$

Question 9

Multiply: $9 y ( 8 y )$

Accepted Answer

A)  $72 y ^ { 2 }$ 
B)  $144 y$ 
C)  72y 
D)  17y 
E)  $17 y ^ { 2 }$ 
A)  $72 y ^ { 2 }$ 
B)  $144 y$ 
C)  72y 
D)  17y 
E)  $17 y ^ { 2 }$

Question 10

Solve the equation below by factoring. $$t ( 3 t + 19 ) = 40$$

Accepted Answer

A)  $t = \frac { 5 } { 3 }$ and $t = - 8$ 
B)  $t = - \frac { 5 } { 3 }$ and $t = 8$ 
C)  $t = \frac { 5 } { 3 }$ and $t = 8$ 
D)  $t = - \frac { 5 } { 3 }$ and $t = - 8$ 
E)  $t = 0 \text { and } t = 19$ 
A)  $t = \frac { 5 } { 3 }$ and $t = - 8$ 
B)  $t = - \frac { 5 } { 3 }$ and $t = 8$ 
C)  $t = \frac { 5 } { 3 }$ and $t = 8$ 
D)  $t = - \frac { 5 } { 3 }$ and $t = - 8$ 
E)  $t = 0 \text { and } t = 19$

Question 11

Rewrite the expression $\frac { 3 w ^ { 3 } } { 5 z ^ { - 3 } }$ using only positive exponents. Assume that z is not zero.

Accepted Answer

A)  $\frac { 27 w ^ { 3 } z ^ { 3 } } { 5 }$ 
B)  $375 w ^ { 3 } z ^ { 3 }$ 
C)  $15 w ^ { 3 } z ^ { 3 }$ 
D)  $\frac { 3 w ^ { 9 } z ^ { 9 } } { 5 }$ 
E)  $\frac { 3 w ^ { 3 } z ^ { 3 } } { 5 }$ 
A)  $\frac { 27 w ^ { 3 } z ^ { 3 } } { 5 }$ 
B)  $375 w ^ { 3 } z ^ { 3 }$ 
C)  $15 w ^ { 3 } z ^ { 3 }$ 
D)  $\frac { 3 w ^ { 9 } z ^ { 9 } } { 5 }$ 
E)  $\frac { 3 w ^ { 3 } z ^ { 3 } } { 5 }$

Question 12

Simplify the expression $\frac { 64 u ^ { 6 } } { 4 u ^ { 2 } }$ . Assume that u is not zero.

Accepted Answer

A)  $16 u ^ { 3 }$ 
B)  $8 u ^ { 4 }$ 
C)  $16 u ^ { 4 }$ 
D)  $8 u ^ { 3 }$ 
E)  $8 u ^ { 8 }$ 
A)  $16 u ^ { 3 }$ 
B)  $8 u ^ { 4 }$ 
C)  $16 u ^ { 4 }$ 
D)  $8 u ^ { 3 }$ 
E)  $8 u ^ { 8 }$

Question 13

The surface area of a right circular cylinder of height 9 units is given by $S = \pi r ^ { 2 } + 18 \pi r$ . Factor this expression.

Accepted Answer

A)  $r ^ { 2 } ( \pi + 18 r )$ 
B)  $r ( r + 18 \pi )$ 
C)  $\pi r ( r + 18 )$ 
D)  $r ^ { 2 } ( \pi + 18 )$ 
E)  $\pi \left( r ^ { 2 } + 18 \right)$ 
A)  $r ^ { 2 } ( \pi + 18 r )$ 
B)  $r ( r + 18 \pi )$ 
C)  $\pi r ( r + 18 )$ 
D)  $r ^ { 2 } ( \pi + 18 )$ 
E)  $\pi \left( r ^ { 2 } + 18 \right)$

Question 14

Use the Zero-Factor Property to solve the equation below. $( x + 5 ) ( 8 x - 1 ) ( x - 4 ) = 0$

Accepted Answer

A)  $x = 5 , x = - \frac { 1 } { 8 } , \text { and } x = 4$ 
B)  $x = - 5 , x = - \frac { 1 } { 8 } , \text { and } x = - 4$ 
C)  $x = - 5 , x = \frac { 1 } { 8 } , \text { and } x = 4$ 
D)  $x = 5 , x = \frac { 1 } { 8 } , \text { and } x = 4$ 
E)  $x = - 5 , x = - \frac { 1 } { 8 } , \text { and } x = 4$ 
A)  $x = 5 , x = - \frac { 1 } { 8 } , \text { and } x = 4$ 
B)  $x = - 5 , x = - \frac { 1 } { 8 } , \text { and } x = - 4$ 
C)  $x = - 5 , x = \frac { 1 } { 8 } , \text { and } x = 4$ 
D)  $x = 5 , x = \frac { 1 } { 8 } , \text { and } x = 4$ 
E)  $x = - 5 , x = - \frac { 1 } { 8 } , \text { and } x = 4$

Question 15

Use the rules of exponents to simplify the expression $\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }$ using only positive exponents. Assume that no variable is zero.

Accepted Answer

A)  $\frac { 64 y ^ { 30 } } { x ^ { 30 } }$ 
B) 1 
C)  $\frac { 64 x ^ { 30 } } { y ^ { 30 } }$ 
D)  $\frac { - 4 y ^ { 30 } } { x ^ { 30 } }$ 
E)  64 
A)  $\frac { 64 y ^ { 30 } } { x ^ { 30 } }$ 
B) 1 
C)  $\frac { 64 x ^ { 30 } } { y ^ { 30 } }$ 
D)  $\frac { - 4 y ^ { 30 } } { x ^ { 30 } }$ 
E)  64

Question 16

Factor the trinomial, if possible. $12 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 }$

Accepted Answer

A)  $2 x ^ { 2 } ( 3 x + 2 ) ( 2 x + 3 )$ 
B)  $2 x ^ { 2 } ( 3 x - 2 ) ( 2 x - 3 )$ 
C)  $2 x ^ { 2 } ( 3 x + 2 ) ( 2 x - 3 )$ 
D)  $2 x ^ { 2 } ( 3 x - 2 ) ( 2 x + 3 )$ 
E) The trinomial is prime. 
A)  $2 x ^ { 2 } ( 3 x + 2 ) ( 2 x + 3 )$ 
B)  $2 x ^ { 2 } ( 3 x - 2 ) ( 2 x - 3 )$ 
C)  $2 x ^ { 2 } ( 3 x + 2 ) ( 2 x - 3 )$ 
D)  $2 x ^ { 2 } ( 3 x - 2 ) ( 2 x + 3 )$ 
E) The trinomial is prime.

Question 17

Find an expression for the area of the figure. Assume all angles are right angles.

Accepted Answer

A)  27 x 
B)  3x 
C)  27x2 
D)  54x2 
E)  40.5x2 
A)  27 x 
B)  3x 
C)  27x2 
D)  54x2 
E)  40.5x2

Question 18

Find the greatest common factor 6.12 and 11 .

Accepted Answer

A) 22 
B) 2 
C) 1 
D) 11 
E) 132 
A) 22 
B) 2 
C) 1 
D) 11 
E) 132

Question 19

Multiply $\left( x ^ { 2 } + 4 x - 4 \right) \left( 5 x ^ { 2 } + 2 \right)$ and simplify.

Accepted Answer

A)  $5 x ^ { 4 } + 8 x - 8$ 
B)  $5 x ^ { 4 } + 24 x ^ { 3 } + 8 x - 8$ 
C)  $5 x ^ { 4 } + 20 x ^ { 3 } - 18 x ^ { 2 } + 8 x - 8$ 
D)  $5 x ^ { 4 } + 20 x ^ { 3 } + 2 x ^ { 2 } - 8$ 
E)  $5 x ^ { 4 } + 24 x ^ { 3 } - 20 x ^ { 2 } + 8 x - 8$ 
A)  $5 x ^ { 4 } + 8 x - 8$ 
B)  $5 x ^ { 4 } + 24 x ^ { 3 } + 8 x - 8$ 
C)  $5 x ^ { 4 } + 20 x ^ { 3 } - 18 x ^ { 2 } + 8 x - 8$ 
D)  $5 x ^ { 4 } + 20 x ^ { 3 } + 2 x ^ { 2 } - 8$ 
E)  $5 x ^ { 4 } + 24 x ^ { 3 } - 20 x ^ { 2 } + 8 x - 8$

Question 20

Find the sum of the polynomials. $\begin{array} { r } 
6 x ^ { 2 } + 7 x - 2 \
7 x ^ { 2 } + 2 x - 2 \
- 6 x - 2 \
\hline
\end{array}$

Accepted Answer

A)  $13 x ^ { 4 } + 3 x ^ { 2 } - 6$ 
B)  $13 x ^ { 2 } + 3 x - 2$ 
C)  $16 x ^ { 7 } - 6$ 
D)  $13 x ^ { 4 } + 3 x ^ { 2 } - 2$ 
E)  $13 x ^ { 2 } + 3 x - 6$ 
A)  $13 x ^ { 4 } + 3 x ^ { 2 } - 6$ 
B)  $13 x ^ { 2 } + 3 x - 2$ 
C)  $16 x ^ { 7 } - 6$ 
D)  $13 x ^ { 4 } + 3 x ^ { 2 } - 2$ 
E)  $13 x ^ { 2 } + 3 x - 6$

Perform the indicated operations and simplify. $2 \left( 4 t ^ { 2 } + 7 \right) - 8 \left( t ^ { 2 } + 7 \right) + 6 \left( 6 t ^ { 2 } + 7 \right)$

Factor the difference of two squares. $v ^ { 2 } - \frac { 81 } { 4 }$

Rewrite the expression $\frac { 1 } { 2 z ^ { - 5 } }$ using only positive exponents. Assume that z is not zero.

Factor the trinomial, if possible. $10 y ^ { 2 } - 29 y - 72$

Find the value of $( - 2 ) ^ { - 5 }$ .

A closed rectangular box has dimensions of length n inches, width n-4 inches, and height n+2 inches. Write a polynomial function $V ( n )$ that represents the volume of the box.

Factor the perfect square trinomial $4 m ^ { 3 } - 72 m ^ { 2 } + 324 m$ .

Use the rules of exponents to simplify the expression $\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$ using only positive exponents. Assume that neither x nor y is 0.

Multiply: $9 y ( 8 y )$

Solve the equation below by factoring. $t ( 3 t + 19 ) = 40$

Rewrite the expression $\frac { 3 w ^ { 3 } } { 5 z ^ { - 3 } }$ using only positive exponents. Assume that z is not zero.

Simplify the expression $\frac { 64 u ^ { 6 } } { 4 u ^ { 2 } }$ . Assume that u is not zero.

The surface area of a right circular cylinder of height 9 units is given by $S = \pi r ^ { 2 } + 18 \pi r$ . Factor this expression.

Use the Zero-Factor Property to solve the equation below. $( x + 5 ) ( 8 x - 1 ) ( x - 4 ) = 0$

Use the rules of exponents to simplify the expression $\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }$ using only positive exponents. Assume that no variable is zero.

Factor the trinomial, if possible. $12 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 }$

Find an expression for the area of the figure. Assume all angles are right angles.

Find the greatest common factor 6.12 and 11 .

Multiply $\left( x ^ { 2 } + 4 x - 4 \right) \left( 5 x ^ { 2 } + 2 \right)$ and simplify.

Find the sum of the polynomials. 6+7x-2 7+2x-2 -6x-2

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Polynomials and Factoring

Perform the indicated operations and simplify. 2(4t2+7)−8(t2+7)+6(6t2+7)2 \left( 4 t ^ { 2 } + 7 \right) - 8 \left( t ^ { 2 } + 7 \right) + 6 \left( 6 t ^ { 2 } + 7 \right)2(4t2+7)−8(t2+7)+6(6t2+7)

Factor the difference of two squares. v2−814v ^ { 2 } - \frac { 81 } { 4 }v2−481​

Rewrite the expression 12z−5\frac { 1 } { 2 z ^ { - 5 } }2z−51​ using only positive exponents. Assume that z is not zero.

Factor the trinomial, if possible. 10y2−29y−7210 y ^ { 2 } - 29 y - 7210y2−29y−72

Find the value of (−2)−5( - 2 ) ^ { - 5 }(−2)−5 .

A closed rectangular box has dimensions of length n inches, width n-4 inches, and height n+2 inches. Write a polynomial function V(n)V ( n )V(n) that represents the volume of the box.

Factor the perfect square trinomial 4m3−72m2+324m4 m ^ { 3 } - 72 m ^ { 2 } + 324 m4m3−72m2+324m .

Use the rules of exponents to simplify the expression (2x4y6)−2\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }(2x4y6)−2 using only positive exponents. Assume that neither x nor y is 0.

Multiply: 9y(8y)9 y ( 8 y )9y(8y)

Solve the equation below by factoring. t(3t+19)=40t ( 3 t + 19 ) = 40t(3t+19)=40

Rewrite the expression 3w35z−3\frac { 3 w ^ { 3 } } { 5 z ^ { - 3 } }5z−33w3​ using only positive exponents. Assume that z is not zero.

Simplify the expression 64u64u2\frac { 64 u ^ { 6 } } { 4 u ^ { 2 } }4u264u6​ . Assume that u is not zero.

The surface area of a right circular cylinder of height 9 units is given by S=πr2+18πrS = \pi r ^ { 2 } + 18 \pi rS=πr2+18πr . Factor this expression.

Use the Zero-Factor Property to solve the equation below. (x+5)(8x−1)(x−4)=0( x + 5 ) ( 8 x - 1 ) ( x - 4 ) = 0(x+5)(8x−1)(x−4)=0

Use the rules of exponents to simplify the expression (2x−5y5)−3(2x−5y5)3\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }(2x−5y5)−3(2x−5y5)3 using only positive exponents. Assume that no variable is zero.

Factor the trinomial, if possible. 12x4−26x3+12x212 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 }12x4−26x3+12x2

Find an expression for the area of the figure. Assume all angles are right angles.

Find the greatest common factor 6.12 and 11 .

Multiply (x2+4x−4)(5x2+2)\left( x ^ { 2 } + 4 x - 4 \right) \left( 5 x ^ { 2 } + 2 \right)(x2+4x−4)(5x2+2) and simplify.

Find the sum of the polynomials. 6+7x-2 7+2x-2 -6x-2

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Perform the indicated operations and simplify. $2 \left( 4 t ^ { 2 } + 7 \right) - 8 \left( t ^ { 2 } + 7 \right) + 6 \left( 6 t ^ { 2 } + 7 \right)$

Factor the difference of two squares. $v ^ { 2 } - \frac { 81 } { 4 }$

Rewrite the expression $\frac { 1 } { 2 z ^ { - 5 } }$ using only positive exponents. Assume that z is not zero.

Factor the trinomial, if possible. $10 y ^ { 2 } - 29 y - 72$

Find the value of $( - 2 ) ^ { - 5 }$ .

A closed rectangular box has dimensions of length n inches, width n-4 inches, and height n+2 inches. Write a polynomial function $V ( n )$ that represents the volume of the box.

Factor the perfect square trinomial $4 m ^ { 3 } - 72 m ^ { 2 } + 324 m$ .

Use the rules of exponents to simplify the expression $\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$ using only positive exponents. Assume that neither x nor y is 0.

Multiply: $9 y ( 8 y )$

Solve the equation below by factoring. $t ( 3 t + 19 ) = 40$

Rewrite the expression $\frac { 3 w ^ { 3 } } { 5 z ^ { - 3 } }$ using only positive exponents. Assume that z is not zero.

Simplify the expression $\frac { 64 u ^ { 6 } } { 4 u ^ { 2 } }$ . Assume that u is not zero.

The surface area of a right circular cylinder of height 9 units is given by $S = \pi r ^ { 2 } + 18 \pi r$ . Factor this expression.

Use the Zero-Factor Property to solve the equation below. $( x + 5 ) ( 8 x - 1 ) ( x - 4 ) = 0$

Use the rules of exponents to simplify the expression $\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }$ using only positive exponents. Assume that no variable is zero.

Factor the trinomial, if possible. $12 x ^ { 4 } - 26 x ^ { 3 } + 12 x ^ { 2 }$

Multiply $\left( x ^ { 2 } + 4 x - 4 \right) \left( 5 x ^ { 2 } + 2 \right)$ and simplify.