Question 1

Factor by grouping.
-  +   + 5r + 5

Accepted Answer

A)  (   + 5)(r - 5) 
B)  (   + 5)(r + 1) 
C)  (   + 5)(r + 5) 
D)  (   + 1)(r + 5) 
A)  (   + 5)(r - 5) 
B)  (   + 5)(r + 1) 
C)  (   + 5)(r + 5) 
D)  (   + 1)(r + 5)

Question 2

Factor the binomial completely. If it is prime, say so.
-25x2 + 16

Accepted Answer

A)  ( 5x + 4)( 5x - 4) 
B)  ( 5x + 4)2  
C)  ( 5x - 4)2  
D)  Prime 
A)  ( 5x + 4)( 5x - 4) 
B)  ( 5x + 4)2  
C)  ( 5x - 4)2  
D)  Prime

Question 3

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-A student is solving the equation x2 = 4x This student has decided to divide both sides of the equation by x and finds the solution x = 4. The student checks the answer in the back of the book and finds that x = 0 is also a solution. The student feels that this is a misprint. How would you advise him or her?

Accepted Answer

Order of operations

Question 4

Complete the factoring.
-x2 - 4x - 32 = (x - 8)( )

Accepted Answer

A)  8 - x 
B)  x + 4 
C)  x - 4 
D)  x2 + 8 
A)  8 - x 
B)  x + 4 
C)  x - 4 
D)  x2 + 8

Question 5

Complete the factoring.
--15     = 5     ( )

Accepted Answer

A)  -75     
B)  -3   
C)  -3     
D)  -75     
A)  -75     
B)  -3   
C)  -3     
D)  -75

Question 6

Factor by grouping.
-54 - 9 x - 6 s + x s

Accepted Answer

A)  ( 6 - x)( 9 + s) 
B)  ( 6 + x)( 9 + s) 
C)  ( 6 + x)( 9 - s) 
D)  ( 6 - x)( 9 - s) 
A)  ( 6 - x)( 9 + s) 
B)  ( 6 + x)( 9 + s) 
C)  ( 6 + x)( 9 - s) 
D)  ( 6 - x)( 9 - s)

Question 7

Solve the problem.
-A long-distance runner runs 4 miles south and then 9 miles east. How far is the runner from the starting point? Round approximations to the nearest tenth.
   
East --9 mi-->

Accepted Answer

A)  4.9 mi 
B)  48.5 mi 
C)  6.5 mi 
D)  9.8 mi 
A)  4.9 mi 
B)  48.5 mi 
C)  6.5 mi 
D)  9.8 mi

Question 8

Factor out the greatest common factor.
-23   - 15

Accepted Answer

A)  2( 11   + 7   ) 
B)  No common factor (except 1) 
C)  3( 7   - 5   ) 
D)  m2( 23 - 15m) 
A)  2( 11   + 7   ) 
B)  No common factor (except 1) 
C)  3( 7   - 5   ) 
D)  m2( 23 - 15m)

Question 9

Factor completely.
-

Accepted Answer

A)      (p + q)(p - 2q) 
B)      (p - 6q)(p + q) 
C)      (p + 6q)(p - 2q) 
D)      (p - 6q)(p + 2q) 
A)      (p + q)(p - 2q) 
B)      (p - 6q)(p + q) 
C)      (p + 6q)(p - 2q) 
D)      (p - 6q)(p + 2q)

Question 10

Factor completely.
-  - 30b + 225

Accepted Answer

A)  (b + 15)(b - 15) 
B)    
C)    
D)  Prime 
A)  (b + 15)(b - 15) 
B)    
C)    
D)  Prime

Question 11

Solve the problem.
-Find three consecutive integers such that the square of the sum of the smaller two is 72 more than the square of the largest.

Accepted Answer

A)  -5, -4, -3 
B)  5, 6, 7, or -5, -4, -3 
C)  5, 6, 7 
D)  3, 5, 7 
A)  -5, -4, -3 
B)  5, 6, 7, or -5, -4, -3 
C)  5, 6, 7 
D)  3, 5, 7

Question 12

Factor by grouping.
-15z2 + 2z - 8

Accepted Answer

A)  ( 3z + 2)( 5z - 4) 
B)  ( 3z - 2)( 5z + 4) 
C)  ( 15z - 2)(z + 4) 
D)  Prime 
A)  ( 3z + 2)( 5z - 4) 
B)  ( 3z - 2)( 5z + 4) 
C)  ( 15z - 2)(z + 4) 
D)  Prime

Question 13

Factor completely.
-33x4y2+54x3y2-24x2y2

Accepted Answer

A)  3     (x + 2)( 11x - 4) 
B)  3(x + 2)( 11x - 4) 
C)  3     (x + 2)( 11x + 4) 
D)      (x - 2)( 11x + 4) 
A)  3     (x + 2)( 11x - 4) 
B)  3(x + 2)( 11x - 4) 
C)  3     (x + 2)( 11x + 4) 
D)      (x - 2)( 11x + 4)

Question 14

Factor completely.
-u2- 2uv - 15v2= (u + 3v)(_____)

Accepted Answer

A)  u + 5v 
B)  u + 5   
C)  u - 5 
D)  u - 5v 
A)  u + 5v 
B)  u + 5   
C)  u - 5 
D)  u - 5v

Question 15

Factor completely.
-x2+3xy-10y2 = (x + 5y)(________)

Accepted Answer

A)  x + 2y 
B)  x - 2y 
C)  x - 2   
D)  x + y 
A)  x + 2y 
B)  x - 2y 
C)  x - 2   
D)  x + y

Question 16

Factor by grouping.
-20x2 - 25xy + 12xy - 15y2

Accepted Answer

A)  ( 5x + 3y)( 4x - 5y) 
B)  ( 5x - 3y)( 4x - 5y) 
C)  ( 5x + 3)( 4x - 5) 
D)  ( 20x + 3y)(x - 5y) 
A)  ( 5x + 3y)( 4x - 5y) 
B)  ( 5x - 3y)( 4x - 5y) 
C)  ( 5x + 3)( 4x - 5) 
D)  ( 20x + 3y)(x - 5y)

Question 17

Factor by grouping.
-12x2 + 25x + 12

Accepted Answer

A)  ( 3x + 4)( 4x + 3) 
B)  ( 12x + 4)(x + 3) 
C)  ( 3x - 4)( 4x - 3) 
D)  Prime 
A)  ( 3x + 4)( 4x + 3) 
B)  ( 12x + 4)(x + 3) 
C)  ( 3x - 4)( 4x - 3) 
D)  Prime

Question 18

Find the greatest common factor of the terms.
-64     , 40

Accepted Answer

A)  8     
B)  4     
C)  320     
D)  8     
A)  8     
B)  4     
C)  320     
D)  8

Question 19

Factor the polynomial completely.
-  - 512

Accepted Answer

A)  (x + 512)(   - 1) 
B)  (x + 8)(   - 8x + 64) 
C)  (x - 8)(   + 8x + 64) 
D)  (x - 8)(   + 64) 
A)  (x + 512)(   - 1) 
B)  (x + 8)(   - 8x + 64) 
C)  (x - 8)(   + 8x + 64) 
D)  (x - 8)(   + 64)

Question 20

Solve the problem.
-A parallelogram has a base of length 2x + 1 and a height of x + 3 and has an area of 42 square units. Find the base and height of the parallelogram. (A = bh)

Accepted Answer

A)  height = 3 units; base = 14 units 
B)  height = 14 units; base = 3 units 
C)  height = 6 units; base = 7 units 
D)  height = 7 units; base = 6 units 
A)  height = 3 units; base = 14 units 
B)  height = 14 units; base = 3 units 
C)  height = 6 units; base = 7 units 
D)  height = 7 units; base = 6 units

Factor by grouping. - + + 5r + 5

Factor the binomial completely. If it is prime, say so. -25x² + 16

Complete the factoring. -x² - 4x - 32 = (x - 8)( )

Complete the factoring. --15 = 5 ( )

Factor by grouping. -54 - 9 x - 6 s + x s

Solve the problem. -A long-distance runner runs 4 miles south and then 9 miles east. How far is the runner from the starting point? Round approximations to the nearest tenth. East --9 mi-->

Factor out the greatest common factor. -23 - 15

Factor completely. -

Factor completely. - - 30b + 225

Solve the problem. -Find three consecutive integers such that the square of the sum of the smaller two is 72 more than the square of the largest.

Factor by grouping. -15z² + 2z - 8

Factor completely. -33x⁴y²+54x³y²-24x²y²

Factor completely. -u²- 2uv - 15v²= (u + 3v)(_____)

Factor completely. -x²+3xy-10y² = (x + 5y)(________)

Factor by grouping. -20x² - 25xy + 12xy - 15y²

Factor by grouping. -12x² + 25x + 12

Find the greatest common factor of the terms. -64 , 40

Factor the polynomial completely. - - 512

Solve the problem. -A parallelogram has a base of length 2x + 1 and a height of x + 3 and has an area of 42 square units. Find the base and height of the parallelogram. (A = bh)

The Real Number System

Linear Equations and Inequalities in One Variable

Linear Equations and Inequalities in Two Variables; Functions

Systems of Linear Equations and Inequalities

Exponents and Polynomials

Factoring and Applications

Roots and Radicals

Quadratic Equations

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Exam 7: Rational Expressions and Applications