Question 1

Factor completely.
-(m + n)   + (m + n)b + 7(m + n)

Accepted Answer

A)  (m + n)(b + 7)(b - 7) 
B)  (m + n)(   + b + 7) 
C)  b(m + n)(b + 8) 
D)  (m + n)(   - b + 7) 
A)  (m + n)(b + 7)(b - 7) 
B)  (m + n)(   + b + 7) 
C)  b(m + n)(b + 8) 
D)  (m + n)(   - b + 7)

Question 2

Choose the one alternative that best completes the statement or answers the question.
-Is it possible to factor the expression 4x6(y + 5) + 9(y - 5)? If so, factor it.

Accepted Answer

A)  Yes: ( 4x6 + 9 + 5 + y) 
B)  Yes: ( 4x6 + 9)(y + 5) 
C)  Yes: ( 4x6 + 9)(y - 5) 
D)  No 
A)  Yes: ( 4x6 + 9 + 5 + y) 
B)  Yes: ( 4x6 + 9)(y + 5) 
C)  Yes: ( 4x6 + 9)(y - 5) 
D)  No

Question 3

Solve the problem. Round to the nearest tenth, if necessary.
-If an object is propelled upward from ground level with an initial velocity of 72.1 feet per second, its height h in feet t seconds later is given by the equation   After how many seconds does the object hit the ground?

Accepted Answer

A)  4.5 sec 
B)  0. 2 sec 
C)  9.0 sec 
D)  2.3 sec 
A)  4.5 sec 
B)  0. 2 sec 
C)  9.0 sec 
D)  2.3 sec

Question 4

Factor out the greatest common factor.
-  + 10x

Accepted Answer

A)    (x + 2) 
B)  5x(x + 2) 
C)  x(5x + 10) 
D)  5x(x + 10) 
A)    (x + 2) 
B)  5x(x + 2) 
C)  x(5x + 10) 
D)  5x(x + 10)

Question 5

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-Tina was asked to solve the following problem: "The product of two consecutive numbers is 90. Find the numbers." Tina's solution is given below. Do you agree with her conclusion? If not, why not?
x(x + 1) = 90
   + x = 90
   + x - 90 = 0
(x + 10)(x - 9) = 0
x = -10 or x = 9
The pair of numbers is 9 and 10

Accepted Answer

There is nothing in the problem to sugge

Question 6

Factor completely.
-  + 8xy + 12

Accepted Answer

A)  (x - 2y)(x - 6y) 
B)  (x + 2y)(x + 6y) 
C)  (x + 2y)(x - 6y) 
D)  x(x + 8y + 12)   
A)  (x - 2y)(x - 6y) 
B)  (x + 2y)(x + 6y) 
C)  (x + 2y)(x - 6y) 
D)  x(x + 8y + 12)

Question 7

Choose the one alternative that best completes the statement or answers the question.
-Find a quadratic equation having the given solutions.x = -   or x =

Accepted Answer

A)  16x2 - 24x - 7 = 0 
B)  4x2 + 6x + 7 = 0 
C)  16x2 + 24x - 7 = 0 
D)  4x2 - 6x - 7 = 0 
A)  16x2 - 24x - 7 = 0 
B)  4x2 + 6x + 7 = 0 
C)  16x2 + 24x - 7 = 0 
D)  4x2 - 6x - 7 = 0

Question 8

Solve the problem.
-The height of a box is 5 inches. The length is three inches more than the width. Find the width if the volume is 440 cubic inches.

Accepted Answer

A)  5 in. 
B)  88 in. 
C)  8 in. 
D)  11 in. 
A)  5 in. 
B)  88 in. 
C)  8 in. 
D)  11 in.

Question 9

Solve the problem. Round to the nearest tenth, if necessary.
-If an object is propelled upward from a height of 112 feet at an initial velocity of 96 feet per second, then its height h after t seconds is given by the equation   After how many seconds does the object hit the ground?

Accepted Answer

A)  7 sec 
B)  11 sec 
C)  3.5 sec 
D)  6.0 sec 
A)  7 sec 
B)  11 sec 
C)  3.5 sec 
D)  6.0 sec

Question 10

Find the greatest common factor of the terms.
-    , x

Accepted Answer

A)  x   
B)      
C)    
D)      
A)  x   
B)      
C)    
D)

Question 11

Complete the factoring.
--72   = -9   ( )

Accepted Answer

A)  648z 
B)  8   
C)  -8   
D)  8   
A)  648z 
B)  8   
C)  -8   
D)  8

Question 12

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-81k2 - 36 = 0

Accepted Answer

A)    
B)  { 6, 0} 
C)    
D)    
A)    
B)  { 6, 0} 
C)    
D)

Question 13

Factor out the greatest common factor.
-2x( 4x + 3) + 5( 4x + 3)

Accepted Answer

A)  ( 2x + 5)( 4x + 3) 
B)  ( 8x + 5)(x + 3) 
C)  ( 8x - 5)(x - 3) 
D)  ( 2x - 5)( 4x - 3) 
A)  ( 2x + 5)( 4x + 3) 
B)  ( 8x + 5)(x + 3) 
C)  ( 8x - 5)(x - 3) 
D)  ( 2x - 5)( 4x - 3)

Question 14

Solve the problem.
-A rectangle has a length of x + 2 and a width of x - 2, and has an area of 60 square units. Find the length and width of the rectangle. (A = LW)

Accepted Answer

A)  width = 3 units; length = 20 units 
B)  width = 4 units; length = 15 units 
C)  width = 6 units; length = 10 units 
D)  width = 5 units; length = 12 units 
A)  width = 3 units; length = 20 units 
B)  width = 4 units; length = 15 units 
C)  width = 6 units; length = 10 units 
D)  width = 5 units; length = 12 units

Question 15

Solve the problem.
-Doris has a rectangular fish pond 9 by 12 feet. She wants to put grass in a strip of uniform width around the pond. She has enough grass seed for 162 square feet. How wide will the strip be?

Accepted Answer

A)  3 ft 
B)  5 ft 
C)  4 ft 
D)  5.5 ft 
A)  3 ft 
B)  5 ft 
C)  4 ft 
D)  5.5 ft

Question 16

Solve the problem.
-A square piece of cardboard is to be formed into an open-topped box by cutting   squares from the corners and folding up the sides. The volume of the resulting box is given by the formula   , where x is the original length of each side of the piece of cardboard. What is the volume of the box if the original length of each side of the piece of cardboard is 16 inches?

Accepted Answer

A)  100   
B)  768   
C)  30   
D)  300   
A)  100   
B)  768   
C)  30   
D)  300

Question 17

Find the greatest common factor of the terms.
-21   , 189

Accepted Answer

A)  21   
B)  189   
C)  21   
D)  3969   
A)  21   
B)  189   
C)  21   
D)  3969

Question 18

Factor completely. If the polynomial is prime, say so.
-

Accepted Answer

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

Question 19

Complete the factoring.
-x2 - 14x + 49 = (x - 7)( )

Accepted Answer

A)  x - 7 
B)  x2 + 7 
C)  x + 7 
D)  7 - x 
A)  x - 7 
B)  x2 + 7 
C)  x + 7 
D)  7 - x

Question 20

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-The height of an object after t seconds is given by the equation   When   , solving for t means finding the time when the object hits the ground. A student uses the quadratic formula and finds 2 solutions. One is negative and the other positive. Which solution makes sense? Which does not? Why?

Accepted Answer

The positive solution makes se

Factor completely. -(m + n) + (m + n)b + 7(m + n)

Choose the one alternative that best completes the statement or answers the question. -Is it possible to factor the expression 4x⁶(y + 5) + 9(y - 5)? If so, factor it.

Solve the problem. Round to the nearest tenth, if necessary. -If an object is propelled upward from ground level with an initial velocity of 72.1 feet per second, its height h in feet t seconds later is given by the equation After how many seconds does the object hit the ground?

Factor out the greatest common factor. - + 10x

Factor completely. - + 8xy + 12

Choose the one alternative that best completes the statement or answers the question. -Find a quadratic equation having the given solutions.x = - or x =

Solve the problem. -The height of a box is 5 inches. The length is three inches more than the width. Find the width if the volume is 440 cubic inches.

Solve the problem. Round to the nearest tenth, if necessary. -If an object is propelled upward from a height of 112 feet at an initial velocity of 96 feet per second, then its height h after t seconds is given by the equation After how many seconds does the object hit the ground?

Find the greatest common factor of the terms. - , x

Complete the factoring. --72 = -9 ( )

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -81k² - 36 = 0

Factor out the greatest common factor. -2x( 4x + 3) + 5( 4x + 3)

Solve the problem. -A rectangle has a length of x + 2 and a width of x - 2, and has an area of 60 square units. Find the length and width of the rectangle. (A = LW)

Solve the problem. -Doris has a rectangular fish pond 9 by 12 feet. She wants to put grass in a strip of uniform width around the pond. She has enough grass seed for 162 square feet. How wide will the strip be?

Find the greatest common factor of the terms. -21 , 189

Factor completely. If the polynomial is prime, say so. -

Complete the factoring. -x² - 14x + 49 = (x - 7)( )

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