Question 1

Multiply Polynomials
-$$( 7 x - 1 ) \left( x ^ { 2 } - 4 x + 1 \right)$$

Accepted Answer

A)  $7 x ^ { 3 } - 29 x ^ { 2 } + 11 x - 1$ 
B)  $7 x ^ { 3 } - 27 x ^ { 2 } + 3 x - 1$ 
C)  $7 x ^ { 3 } - 28 x ^ { 2 } + 7 x + 1$ 
D)  $7 x ^ { 3 } + 29 x ^ { 2 } - 11 x + 1$ 
A)  $7 x ^ { 3 } - 29 x ^ { 2 } + 11 x - 1$ 
B)  $7 x ^ { 3 } - 27 x ^ { 2 } + 3 x - 1$ 
C)  $7 x ^ { 3 } - 28 x ^ { 2 } + 7 x + 1$ 
D)  $7 x ^ { 3 } + 29 x ^ { 2 } - 11 x + 1$ A

Question 2

Use FOIL in Polynomial Multiplication
-$$\left( 7 x ^ { 2 } - 2 \right) \left( 9 x ^ { 2 } - 1 \right)$$

Accepted Answer

A)  $63 x ^ { 4 } - 25 x ^ { 2 } + 2$ 
B)  $16 x ^ { 4 } - 25 x ^ { 2 } + 2$ 
C)  $63 x ^ { 4 } - 25 x ^ { 2 } - 25$ 
D)  $63 x ^ { 2 } - 25 x + 2$ 
A)  $63 x ^ { 4 } - 25 x ^ { 2 } + 2$ 
B)  $16 x ^ { 4 } - 25 x ^ { 2 } + 2$ 
C)  $63 x ^ { 4 } - 25 x ^ { 2 } - 25$ 
D)  $63 x ^ { 2 } - 25 x + 2$ A

Question 3

Evaluate the algebraic expression for the given value or values of the variable(s).
-$$\frac { 6 ( x + 3 ) } { 2 x + 2 } ; \quad x = 5$$

Accepted Answer

A)  4 
B)  1 
C)  8 
D)  $\frac { 11 } { 2 }$ 
A)  4 
B)  1 
C)  8 
D)  $\frac { 11 } { 2 }$ A

Question 4

Use Scientific Notation
-$2 \times 10 ^ { 5 }$

Accepted Answer

A)  $200,000$ 
B)  $0.00002$ 
C)  $2000.000$ 
D)  $0.000002$ 
A)  $200,000$ 
B)  $0.00002$ 
C)  $2000.000$ 
D)  $0.000002$

Question 5

Add and Subtract Rational Expressions
-$$\frac { 2 } { x ^ { 2 } - 3 x + 2 } + \frac { 7 } { x ^ { 2 } - 1 }$$

Accepted Answer

A)  $\frac { 9 x - 12 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
B)  $\frac { 9 x - 12 } { ( x - 1 ) ( x - 2 ) }$ 
C)  $\frac { 12 x - 9 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
D)  $\frac { 28 x - 12 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
A)  $\frac { 9 x - 12 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
B)  $\frac { 9 x - 12 } { ( x - 1 ) ( x - 2 ) }$ 
C)  $\frac { 12 x - 9 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$ 
D)  $\frac { 28 x - 12 } { ( x - 1 ) ( x + 1 ) ( x - 2 ) }$

Question 6

Use the Power Rule
-$$\left( x ^ { 7 } \right) ^ { 8 }$$

Accepted Answer

A)  $x ^ { 56 }$ 
B)  $x$ 
C)  $8 x ^ { 7 }$ 
D)  $8 x ^ { 56 }$ 
A)  $x ^ { 56 }$ 
B)  $x$ 
C)  $8 x ^ { 7 }$ 
D)  $8 x ^ { 56 }$

Question 7

Simplify Complex Rational Expressions
-$$\frac { \frac { 1 } { x + 6 } } { \frac { 5 } { x ^ { 2 } - 36 } }$$

Accepted Answer

A)  $\frac { x - 6 } { 5 }$ 
B)  $\frac { x + 6 } { 5 }$ 
C)  $x - 6$ 
D)  $\frac { 5 } { x - 6 }$ 
A)  $\frac { x - 6 } { 5 }$ 
B)  $\frac { x + 6 } { 5 }$ 
C)  $x - 6$ 
D)  $\frac { 5 } { x - 6 }$

Question 8

Add and Subtract Rational Expressions
-$$\frac { x - 5 } { x ^ { 2 } + 12 x + 32 } + \frac { 2 x + 7 } { x ^ { 2 } + 9 x + 20 }$$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 23 x + 31 } { ( x + 4 ) ( x + 8 ) ( x + 5 ) }$ 
B)  $\frac { 3 x ^ { 2 } + 23 x + 31 } { ( x - 4 ) ( x - 8 ) ( x - 5 ) }$ 
C)  $\frac { 3 x + 2 } { 2 x ^ { 2 } + 21 x + 52 }$ 
D)  $3 x + 2$ 
A)  $\frac { 3 x ^ { 2 } + 23 x + 31 } { ( x + 4 ) ( x + 8 ) ( x + 5 ) }$ 
B)  $\frac { 3 x ^ { 2 } + 23 x + 31 } { ( x - 4 ) ( x - 8 ) ( x - 5 ) }$ 
C)  $\frac { 3 x + 2 } { 2 x ^ { 2 } + 21 x + 52 }$ 
D)  $3 x + 2$

Question 9

Identify Properties of the Real Numbers
-$- ( - 9 + 5 y )$

Accepted Answer

A)  $9 - 5 y$ 
B)  $9 + 5 y$ 
C)  $- 9 + 5 y$ 
D)  $45 \mathrm { y }$ 
A)  $9 - 5 y$ 
B)  $9 + 5 y$ 
C)  $- 9 + 5 y$ 
D)  $45 \mathrm { y }$

Question 10

Use FOIL in Polynomial Multiplication
-Write a polynomial in standard form that represents the area of the shaded region.

Accepted Answer

A)  $3 x + 11$ 
B)  $17 x + 31$ 
C)  $x ^ { 2 } + 14 x + 11$ 
D)  $- 3 x - 11$ 
A)  $3 x + 11$ 
B)  $17 x + 31$ 
C)  $x ^ { 2 } + 14 x + 11$ 
D)  $- 3 x - 11$

Question 11

Use Special Products in Polynomial Multiplication
-$$\left( 1 + x ^ { 3 } \right) \left( 1 - x ^ { 3 } \right)$$

Accepted Answer

A)  $1 - x ^ { 6 }$ 
B)  $2 - x ^ { 6 }$ 
C)  $2 - x ^ { 9 }$ 
D)  $1 - x ^ { 9 }$ 
A)  $1 - x ^ { 6 }$ 
B)  $2 - x ^ { 6 }$ 
C)  $2 - x ^ { 9 }$ 
D)  $1 - x ^ { 9 }$

Question 12

Simplify Exponential Expressions
-$$\left( - 5 x ^ { 4 } y ^ { - 5 } \right) \left( 3 x ^ { - 1 } y \right)$$

Accepted Answer

A)  $\frac { - 15 x ^ { 3 } } { y ^ { 4 } }$ 
B)  $- 15 x ^ { 3 } y ^ { 6 }$ 
C)  $\frac { - 2 x ^ { 3 } } { y ^ { 4 } }$ 
D)  $\frac { - 15 x ^ { 5 } } { y ^ { 6 } }$ 
A)  $\frac { - 15 x ^ { 3 } } { y ^ { 4 } }$ 
B)  $- 15 x ^ { 3 } y ^ { 6 }$ 
C)  $\frac { - 2 x ^ { 3 } } { y ^ { 4 } }$ 
D)  $\frac { - 15 x ^ { 5 } } { y ^ { 6 } }$

Question 13

Evaluate Absolute Value
-$| \sqrt { 10 } - 13 |$

Accepted Answer

A)  $13 - \sqrt { 10 }$ 
B)  $\sqrt { 10 } - 13$ 
C)  $- 3$ 
D)  3 )3 
A)  $13 - \sqrt { 10 }$ 
B)  $\sqrt { 10 } - 13$ 
C)  $- 3$ 
D)  3 )3

Question 14

Use Special Products in Polynomial Multiplication
-$$( 6 x - 1 ) ^ { 2 }$$

Accepted Answer

A)  $36 x ^ { 2 } - 12 x + 1$ 
B)  $36 x ^ { 2 } + 1$ 
C)  $6 x ^ { 2 } - 12 x + 1$ 
D)  $6 x ^ { 2 } + 1$ 
A)  $36 x ^ { 2 } - 12 x + 1$ 
B)  $36 x ^ { 2 } + 1$ 
C)  $6 x ^ { 2 } - 12 x + 1$ 
D)  $6 x ^ { 2 } + 1$

Question 15

Use the Product Rule to Simplify Square Roots
-The formula $\mathrm { v } = \sqrt { 2.5 \mathrm { r } }$ models the safe maximum speed, $\mathrm { v }$, in miles per hour, at which a car can travel on a curved road with radius of curvature, $r$, in feet. A highway crew measures the radius of curvature at an exit ramp as 490 feet. What is the maximum safe speed?

Accepted Answer

A)  35 miles per hour 
B)  49 miles per hour 
C)  40 miles per hour 
D)  32 miles per hour 
A)  35 miles per hour 
B)  49 miles per hour 
C)  40 miles per hour 
D)  32 miles per hour

Question 16

Rationalize Denominators
-$\frac { \sqrt { 144 } } { \sqrt { 11 } }$

Accepted Answer

A)  $\frac { 12 \sqrt { 11 } } { 11 }$ 
B)  $12 \sqrt { 11 }$ 
C)  $\frac { 144 \sqrt { 11 } } { 11 }$ 
D)  133 
A)  $\frac { 12 \sqrt { 11 } } { 11 }$ 
B)  $12 \sqrt { 11 }$ 
C)  $\frac { 144 \sqrt { 11 } } { 11 }$ 
D)  133

Question 17

Factor the Difference of Squares
-$\left( 16 x ^ { 4 } - 81 \right)$

Accepted Answer

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

Question 18

Factor Trinomials
-$x ^ { 2 } - 2 x y - 63 y ^ { 2 }$

Accepted Answer

A)  $( x + 7 y ) ( x - 9 y )$ 
B)  $( x - 7 y ) ( x - 9 y )$ 
C)  $( x - 7 y ) ( x + y )$ 
D)  prime 
A)  $( x + 7 y ) ( x - 9 y )$ 
B)  $( x - 7 y ) ( x - 9 y )$ 
C)  $( x - 7 y ) ( x + y )$ 
D)  prime

Question 19

Simplify Complex Rational Expressions
-$$\frac { \frac { x } { x - 2 } + 1 } { \frac { 3 } { x ^ { 2 } - 4 } + 1 }$$

Accepted Answer

A)  $\frac { 2 x + 4 } { x + 1 }$ 
B)  $\frac { x + 2 } { x + 1 }$ 
C)  $\frac { 2 x + 4 } { x - 1 }$ 
D)  $\frac { 2 x - 4 } { x - 1 }$ 
A)  $\frac { 2 x + 4 } { x + 1 }$ 
B)  $\frac { x + 2 } { x + 1 }$ 
C)  $\frac { 2 x + 4 } { x - 1 }$ 
D)  $\frac { 2 x - 4 } { x - 1 }$

Question 20

Add and Subtract Rational Expressions
-$$\frac { 5 x + 3 } { 5 x + 6 } + \frac { 5 x + 9 } { 5 x + 6 }$$

Accepted Answer

A)  2 
B)  1 
C)  $\frac { 6 x + 7 } { 5 x + 6 }$ 
D)  $\frac { 2 } { 5 x + 6 }$ 
A)  2 
B)  1 
C)  $\frac { 6 x + 7 } { 5 x + 6 }$ 
D)  $\frac { 2 } { 5 x + 6 }$

Multiply Polynomials - $( 7 x - 1 ) \left( x ^ { 2 } - 4 x + 1 \right)$

Use FOIL in Polynomial Multiplication - $\left( 7 x ^ { 2 } - 2 \right) \left( 9 x ^ { 2 } - 1 \right)$

Evaluate the algebraic expression for the given value or values of the variable(s). - $\frac { 6 ( x + 3 ) } { 2 x + 2 } ; \quad x = 5$

Use Scientific Notation - $2 \times 10 ^ { 5 }$

Add and Subtract Rational Expressions - $\frac { 2 } { x ^ { 2 } - 3 x + 2 } + \frac { 7 } { x ^ { 2 } - 1 }$

Use the Power Rule - $\left( x ^ { 7 } \right) ^ { 8 }$

Simplify Complex Rational Expressions - $\frac { \frac { 1 } { x + 6 } } { \frac { 5 } { x ^ { 2 } - 36 } }$

Add and Subtract Rational Expressions - $\frac { x - 5 } { x ^ { 2 } + 12 x + 32 } + \frac { 2 x + 7 } { x ^ { 2 } + 9 x + 20 }$

Identify Properties of the Real Numbers - $- ( - 9 + 5 y )$

Use FOIL in Polynomial Multiplication -Write a polynomial in standard form that represents the area of the shaded region.

Use Special Products in Polynomial Multiplication - $\left( 1 + x ^ { 3 } \right) \left( 1 - x ^ { 3 } \right)$

Simplify Exponential Expressions - $\left( - 5 x ^ { 4 } y ^ { - 5 } \right) \left( 3 x ^ { - 1 } y \right)$

Evaluate Absolute Value - $| \sqrt { 10 } - 13 |$

Use Special Products in Polynomial Multiplication - $( 6 x - 1 ) ^ { 2 }$

Rationalize Denominators - $\frac { \sqrt { 144 } } { \sqrt { 11 } }$

Factor the Difference of Squares - $\left( 16 x ^ { 4 } - 81 \right)$

Factor Trinomials - $x ^ { 2 } - 2 x y - 63 y ^ { 2 }$

Simplify Complex Rational Expressions - $\frac { \frac { x } { x - 2 } + 1 } { \frac { 3 } { x ^ { 2 } - 4 } + 1 }$

Add and Subtract Rational Expressions - $\frac { 5 x + 3 } { 5 x + 6 } + \frac { 5 x + 9 } { 5 x + 6 }$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Filters

Exam 12: Prerequisites: Fundamental Concepts of Algebra

Multiply Polynomials - (7x−1)(x2−4x+1)( 7 x - 1 ) \left( x ^ { 2 } - 4 x + 1 \right)(7x−1)(x2−4x+1)

Use FOIL in Polynomial Multiplication - (7x2−2)(9x2−1)\left( 7 x ^ { 2 } - 2 \right) \left( 9 x ^ { 2 } - 1 \right)(7x2−2)(9x2−1)

Evaluate the algebraic expression for the given value or values of the variable(s). - 6(x+3)2x+2;x=5\frac { 6 ( x + 3 ) } { 2 x + 2 } ; \quad x = 52x+26(x+3)​;x=5

Use Scientific Notation - 2×1052 \times 10 ^ { 5 }2×105

Add and Subtract Rational Expressions - 2x2−3x+2+7x2−1\frac { 2 } { x ^ { 2 } - 3 x + 2 } + \frac { 7 } { x ^ { 2 } - 1 }x2−3x+22​+x2−17​

Use the Power Rule - (x7)8\left( x ^ { 7 } \right) ^ { 8 }(x7)8

Simplify Complex Rational Expressions - 1x+65x2−36\frac { \frac { 1 } { x + 6 } } { \frac { 5 } { x ^ { 2 } - 36 } }x2−365​x+61​​

Add and Subtract Rational Expressions - x−5x2+12x+32+2x+7x2+9x+20\frac { x - 5 } { x ^ { 2 } + 12 x + 32 } + \frac { 2 x + 7 } { x ^ { 2 } + 9 x + 20 }x2+12x+32x−5​+x2+9x+202x+7​

Identify Properties of the Real Numbers - −(−9+5y)- ( - 9 + 5 y )−(−9+5y)