Question 1

Factor by grouping.
-$$6 x ^ { 2 } - 8 x + 15 x - 20$$

Accepted Answer

A)  $( 6 x - 5 ) ( x + 4 )$ 
B)  $( 2 x - 5 ) ( 3 x + 4 )$ 
C)  $( 6 x + 5 ) ( x - 4 )$ 
D)  $( 2 x + 5 ) ( 3 x - 4 )$ 
A)  $( 6 x - 5 ) ( x + 4 )$ 
B)  $( 2 x - 5 ) ( 3 x + 4 )$ 
C)  $( 6 x + 5 ) ( x - 4 )$ 
D)  $( 2 x + 5 ) ( 3 x - 4 )$

Question 2

Factor out the greatest common factor. Simplify the factors, if possible.
-$$5 x ^ { 3 } + 25 x$$

Accepted Answer

A)  $5 x \left( x ^ { 2 } + 20 x \right)$ 
B)  $5 x ^ { 2 } ( x + 5 )$ 
C)  $5 x \left( x ^ { 2 } + 5 \right)$ 
D)  $5 x \left( x ^ { 2 } + 5 x \right)$ 
A)  $5 x \left( x ^ { 2 } + 20 x \right)$ 
B)  $5 x ^ { 2 } ( x + 5 )$ 
C)  $5 x \left( x ^ { 2 } + 5 \right)$ 
D)  $5 x \left( x ^ { 2 } + 5 x \right)$

Question 3

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$$

Accepted Answer

A)  $343 p ^ { 3 } + 1$ 
B)  $343 p ^ { 3 } + 56 p ^ { 2 } - 1$ 
C)  $49 p ^ { 3 } - 1$ 
D)  $343 p ^ { 3 } - 1$ 
A)  $343 p ^ { 3 } + 1$ 
B)  $343 p ^ { 3 } + 56 p ^ { 2 } - 1$ 
C)  $49 p ^ { 3 } - 1$ 
D)  $343 p ^ { 3 } - 1$

Question 4

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

Accepted Answer

A)  $( 3 x + y ) ( x + y )$ 
B)  $( 3 x - y ) ( x - y )$ 
C)  prime 
D)  $( 3 x + y ) ( x + 3 y )$ 
A)  $( 3 x + y ) ( x + y )$ 
B)  $( 3 x - y ) ( x - y )$ 
C)  prime 
D)  $( 3 x + y ) ( x + 3 y )$

Question 5

Factor by any method.
-$$6 x ^ { 4 } + 13 x ^ { 2 } + 6$$

Accepted Answer

A)  $\left( 6 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$ 
B)  $\left( 2 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } + 6 \right)$ 
C)  $\left( 2 x ^ { 2 } + 3 \right) \left( 3 x ^ { 2 } + 2 \right)$ 
D)  $\left( 3 x ^ { 2 } - 2 \right) \left( 2 x ^ { 2 } - 3 \right)$ 
A)  $\left( 6 x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 2 \right)$ 
B)  $\left( 2 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } + 6 \right)$ 
C)  $\left( 2 x ^ { 2 } + 3 \right) \left( 3 x ^ { 2 } + 2 \right)$ 
D)  $\left( 3 x ^ { 2 } - 2 \right) \left( 2 x ^ { 2 } - 3 \right)$

Question 6

Solve the problem.
-$$\frac { - 8 x ^ { 10 } + 40 x ^ { 6 } } { - 4 x ^ { 2 } }$$

Accepted Answer

A)  $2 x ^ { 8 } - 10 x ^ { 4 }$ 
B)  $- 8 x ^ { 10 } - 10 x ^ { 4 }$ 
C)  $- 8 x ^ { 14 }$ 
D)  $2 x ^ { 8 } + 40 x ^ { 6 }$ 
A)  $2 x ^ { 8 } - 10 x ^ { 4 }$ 
B)  $- 8 x ^ { 10 } - 10 x ^ { 4 }$ 
C)  $- 8 x ^ { 14 }$ 
D)  $2 x ^ { 8 } + 40 x ^ { 6 }$

Question 7

Solve the problem.
-A simple exercise machine can be constructed by mounting a stiff spring securely to a wall and attaching a "T" handle to the free end of the spring. The arms can be exercised simply by pulling the "T" handle towards the torso. For a particular spring, the stretch distance is related to the work exerted by the equation $x = \sqrt { \frac { 2 W } { 85000 } }$, where $W$ is the work exerted in joules and $x$ is the stretch distance in $\mathrm { cm }$. How far will you stretch the spring if you exert 638 joules of work? Round your answer to three decimal places.

Accepted Answer

A)  $0.015 \mathrm {~cm}$ 
B)  $0.087 \mathrm {~cm}$ 
C)  $0.130 \mathrm {~cm}$ 
D)  $0.123 \mathrm {~cm}$ 
A)  $0.015 \mathrm {~cm}$ 
B)  $0.087 \mathrm {~cm}$ 
C)  $0.130 \mathrm {~cm}$ 
D)  $0.123 \mathrm {~cm}$

Question 8

Write in exponential form. Assume all variables are positive real numbers.
-$$- \sqrt { 108 m ^ { 11 } }$$

Accepted Answer

A)  $- 108 m ^ { 11 / 2 }$ 
B)  $- 11,664 \mathrm {~m}^{2 / 11}$ 
C)  $- 108 ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
D)  $108 \mathrm {~m} ^ { 2 / 11 }$ 
A)  $- 108 m ^ { 11 / 2 }$ 
B)  $- 11,664 \mathrm {~m}^{2 / 11}$ 
C)  $- 108 ^ { 1 / 2 } \mathrm {~m} ^ { 11 / 2 }$ 
D)  $108 \mathrm {~m} ^ { 2 / 11 }$

Question 9

Write in radical form. Assume all variables represent positive real numbers.
-$( 2 x ) ^ { 1 / 5 }$

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 5 ] { 2 x } }$ 
B)  $\sqrt [ 5 ] { 2 \mathrm { x } }$ 
C)  $\frac { \sqrt { 2 x } } { 5 }$ 
D)  $\sqrt [ 1 / 5 ] { 2 x }$ 
A)  $\frac { 1 } { \sqrt [ 5 ] { 2 x } }$ 
B)  $\sqrt [ 5 ] { 2 \mathrm { x } }$ 
C)  $\frac { \sqrt { 2 x } } { 5 }$ 
D)  $\sqrt [ 1 / 5 ] { 2 x }$

Question 10

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-As the relative humidity increases, the temperature seems higher than it is. The formula T = 0.113x + 87.16 approximates the apparent temperature for an actual temperature of 95°F, where x is the
Relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity
Of 60%?

Accepted Answer

A)  591°F 
B)  87°F 
C)  94°F 
D)  147°F 
A)  591°F 
B)  87°F 
C)  94°F 
D)  147°F

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt { 45 k ^ { 7 } q ^ { 8 } }$$

Accepted Answer

A)  $3 k ^ { 7 } q ^ { 8 } \sqrt { 5 k }$ 
B)  $3 k ^ { 3 } q 4 \sqrt { 5 k }$ 
C)  $3 q ^ { 4 } \sqrt { 5 \mathrm { k } ^ { 7 } }$ 
D)  $3 k ^ { 3 } q ^ { 4 } \sqrt { 5 }$ 
A)  $3 k ^ { 7 } q ^ { 8 } \sqrt { 5 k }$ 
B)  $3 k ^ { 3 } q 4 \sqrt { 5 k }$ 
C)  $3 q ^ { 4 } \sqrt { 5 \mathrm { k } ^ { 7 } }$ 
D)  $3 k ^ { 3 } q ^ { 4 } \sqrt { 5 }$

Question 12

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- x ^ { - 4 }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 4 } }$ 
B)  $4 x$ 
C)  $- 4 x$ 
D)  $- \frac { 1 } { x ^ { 4 } }$ 
A)  $\frac { 1 } { x ^ { 4 } }$ 
B)  $4 x$ 
C)  $- 4 x$ 
D)  $- \frac { 1 } { x ^ { 4 } }$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$- 8 \sqrt { 5 } + 19 \sqrt { 5 }$

Accepted Answer

A)  $- 12 \sqrt { 5 }$ 
B)  $11 \sqrt { 5 }$ 
C)  $28 \sqrt { 5 }$ 
D)  $- 27 \sqrt { 5 }$ 
A)  $- 12 \sqrt { 5 }$ 
B)  $11 \sqrt { 5 }$ 
C)  $28 \sqrt { 5 }$ 
D)  $- 27 \sqrt { 5 }$

Question 14

Solve the problem.
-$$( p + 11 q ) ( p - 11 q )$$

Accepted Answer

A)  $p ^ { 2 } - 22 p q - 121 q ^ { 2 }$ 
B)  $\mathrm { p } ^ { 2 } - 22 \mathrm { q } ^ { 2 }$ 
C)  $\mathrm { p } ^ { 2 } - 121 \mathrm { q } ^ { 2 }$ 
D)  $p ^ { 2 } + 22 p q - 121 q ^ { 2 }$ 
A)  $p ^ { 2 } - 22 p q - 121 q ^ { 2 }$ 
B)  $\mathrm { p } ^ { 2 } - 22 \mathrm { q } ^ { 2 }$ 
C)  $\mathrm { p } ^ { 2 } - 121 \mathrm { q } ^ { 2 }$ 
D)  $p ^ { 2 } + 22 p q - 121 q ^ { 2 }$

Question 15

Find the distance between two points given their coordinates.
-Find the distance between points R and S on a number line, with coordinates -6 and -11, respectively.

Accepted Answer

A)  d(R, S) = -17 
B)  d(R, S) = 17 
C)  d(R, S) = -5 
D)  d(R, S) = 5 
A)  d(R, S) = -17 
B)  d(R, S) = 17 
C)  d(R, S) = -5 
D)  d(R, S) = 5

Question 16

Round to two decimal places unless otherwise indicated.
If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the
-If the average cost per unit $\mathrm { C } ( \mathrm { x } )$ to produce $\mathrm { x }$ units of plywood is given by $\mathrm { C } ( \mathrm { x } ) = \frac { 900 } { \mathrm { x } + 30 }$, what do 1000 units cost?

Accepted Answer

A)  $\$ 400.00$ 
B)  $\$ 899.97$ 
C)  $\$ 30000.00$ 
D)  $\$ 873.79$ 
A)  $\$ 400.00$ 
B)  $\$ 899.97$ 
C)  $\$ 30000.00$ 
D)  $\$ 873.79$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - 8 }$$

Accepted Answer

A)  $- 2$ 
B)  4 
C)  not a real number 
D)  $\pm 2$ 
A)  $- 2$ 
B)  4 
C)  not a real number 
D)  $\pm 2$

Question 18

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( \frac { x ^ { 4 } } { y ^ { - 8 } } \right) ^ { 1 / 4 }$$

Accepted Answer

A)  $x y ^ { 1 / 2 }$ 
B)  $x y ^ { 2 }$ 
C)  $x y$ 
D)  $\frac { x } { y ^ { 2 } }$ 
A)  $x y ^ { 1 / 2 }$ 
B)  $x y ^ { 2 }$ 
C)  $x y$ 
D)  $\frac { x } { y ^ { 2 } }$

Question 19

Factor the trinomial, if possible.
-$$- 2 x ^ { 3 } + 2 x ^ { 2 } + 60 x$$

Accepted Answer

A)  $- 2 x ^ { 2 } ( x - 6 ) ( x - 5 )$ 
B)  $- 2 x ( x - 6 ) ( x + 5 )$ 
C)  $2 x ( x + 6 ) ( x + 5 )$ 
D)  $- 2 x ( x + 6 ) ( x - 5 )$ 
A)  $- 2 x ^ { 2 } ( x - 6 ) ( x - 5 )$ 
B)  $- 2 x ( x - 6 ) ( x + 5 )$ 
C)  $2 x ( x + 6 ) ( x + 5 )$ 
D)  $- 2 x ( x + 6 ) ( x - 5 )$

Question 20

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$\left( 4 x ^ { 2 } + 3 x + 4 \right) \left( x ^ { 2 } + 5 x - 4 \right)$

Accepted Answer

A)  $4 x ^ { 4 } + 20 x ^ { 3 } + 3 x ^ { 2 } + 8 x - 16$ 
B)  $4 x ^ { 4 } + 20 x ^ { 3 } - 1 x ^ { 2 } + 8 x - 16$ 
C)  $4 x ^ { 4 } + 23 x ^ { 3 } - 1 x ^ { 2 } + 8 x - 16$ 
D)  $4 x ^ { 4 } + 23 x ^ { 3 } + 3 x ^ { 2 } + 8 x - 16$ 
A)  $4 x ^ { 4 } + 20 x ^ { 3 } + 3 x ^ { 2 } + 8 x - 16$ 
B)  $4 x ^ { 4 } + 20 x ^ { 3 } - 1 x ^ { 2 } + 8 x - 16$ 
C)  $4 x ^ { 4 } + 23 x ^ { 3 } - 1 x ^ { 2 } + 8 x - 16$ 
D)  $4 x ^ { 4 } + 23 x ^ { 3 } + 3 x ^ { 2 } + 8 x - 16$

Factor by grouping. - $6 x ^ { 2 } - 8 x + 15 x - 20$

Factor out the greatest common factor. Simplify the factors, if possible. - $5 x ^ { 3 } + 25 x$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)$

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

Factor by any method. - $6 x ^ { 4 } + 13 x ^ { 2 } + 6$

Solve the problem. - $\frac { - 8 x ^ { 10 } + 40 x ^ { 6 } } { - 4 x ^ { 2 } }$

Write in exponential form. Assume all variables are positive real numbers. - $- \sqrt { 108 m ^ { 11 } }$

Write in radical form. Assume all variables represent positive real numbers. - $( 2 x ) ^ { 1 / 5 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 45 k ^ { 7 } q ^ { 8 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- x ^ { - 4 }$

Simplify the expression. Assume all variables represent positive real numbers. - $- 8 \sqrt { 5 } + 19 \sqrt { 5 }$

Solve the problem. - $( p + 11 q ) ( p - 11 q )$

Find the distance between two points given their coordinates. -Find the distance between points R and S on a number line, with coordinates -6 and -11, respectively.

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 8 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { x ^ { 4 } } { y ^ { - 8 } } \right) ^ { 1 / 4 }$

Factor the trinomial, if possible. - $- 2 x ^ { 3 } + 2 x ^ { 2 } + 60 x$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $\left( 4 x ^ { 2 } + 3 x + 4 \right) \left( x ^ { 2 } + 5 x - 4 \right)$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 1: Review of Basic Concepts

Factor by grouping. - 6x2−8x+15x−206 x ^ { 2 } - 8 x + 15 x - 206x2−8x+15x−20

Factor out the greatest common factor. Simplify the factors, if possible. - 5x3+25x5 x ^ { 3 } + 25 x5x3+25x

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - (7p−1)(49p2+7p+1)( 7 p - 1 ) \left( 49 p ^ { 2 } + 7 p + 1 \right)(7p−1)(49p2+7p+1)

Factor the trinomial, if possible. - 3x2+4xy+y23 x ^ { 2 } + 4 x y + y ^ { 2 }3x2+4xy+y2

Factor by any method. - 6x4+13x2+66 x ^ { 4 } + 13 x ^ { 2 } + 66x4+13x2+6

Solve the problem. - −8x10+40x6−4x2\frac { - 8 x ^ { 10 } + 40 x ^ { 6 } } { - 4 x ^ { 2 } }−4x2−8x10+40x6​

Write in exponential form. Assume all variables are positive real numbers. - −108m11- \sqrt { 108 m ^ { 11 } }−108m11​

Write in radical form. Assume all variables represent positive real numbers. - (2x)1/5( 2 x ) ^ { 1 / 5 }(2x)1/5

Simplify the expression. Assume all variables represent positive real numbers. - 45k7q8\sqrt { 45 k ^ { 7 } q ^ { 8 } }45k7q8​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −x−4- x ^ { - 4 }−x−4

Simplify the expression. Assume all variables represent positive real numbers. - −85+195- 8 \sqrt { 5 } + 19 \sqrt { 5 }−85​+195​

Solve the problem. - (p+11q)(p−11q)( p + 11 q ) ( p - 11 q )(p+11q)(p−11q)