Question 1

Factor by grouping.
-8x2 + 14xt + 3t2

Accepted Answer

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

Question 2

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-6x(x + 6) = (2x + 8)(x + 6)

Accepted Answer

A)  { 6, 4} 
B)  { -6, 2} 
C)  { 6, 2} 
D)  { -6, 4} 
A)  { 6, 4} 
B)  { -6, 2} 
C)  { 6, 2} 
D)  { -6, 4}

Question 3

Complete the factoring.
-    + 28     = 7     ( )

Accepted Answer

A)  y + 4   
B)  y + 4   
C)  y + 4 
D)  7y + 4x 
A)  y + 4   
B)  y + 4   
C)  y + 4 
D)  7y + 4x

Question 4

Find the pair of numbers whose product and sum are given.
-Product: -45 Sum: -4

Accepted Answer

A)  45 and -1 
B)  9 and -5 
C)  -9 and 5 
D)  -45 and 1 
A)  45 and -1 
B)  9 and -5 
C)  -9 and 5 
D)  -45 and 1

Question 5

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-(x - 8)(x + 7) = 0

Accepted Answer

A)  { 8, -8, 7, -7} 
B)  {-8, 7} 
C)  { 8, 7} 
D)  { 8, -7} 
A)  { 8, -8, 7, -7} 
B)  {-8, 7} 
C)  { 8, 7} 
D)  { 8, -7}

Question 6

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-Why is 5 called a triple solution to the equation (x - 5)3 = 0?

Accepted Answer

(x - 5)³ = (x - 5)(x

Question 7

Factor completely. If the polynomial cannot be factored, write prime.
-x2 - x - 30

Accepted Answer

A)  (x + 5)(x - 6) 
B)  (x + 1)(x - 30) 
C)  (x + 6)(x - 5) 
D)  Prime 
A)  (x + 5)(x - 6) 
B)  (x + 1)(x - 30) 
C)  (x + 6)(x - 5) 
D)  Prime

Question 8

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-24p4 - 25p2 = 10p3

Accepted Answer

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

Question 9

Factor completely.
-3x2 - 3x - 18

Accepted Answer

A)  3(x - 2)(x + 3) 
B)  Prime 
C)  ( 3x + 6)(x - 3) 
D)  3(x + 2)(x - 3) 
A)  3(x - 2)(x + 3) 
B)  Prime 
C)  ( 3x + 6)(x - 3) 
D)  3(x + 2)(x - 3)

Question 10

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-(x + 8)(   - 9x + 14) = 0

Accepted Answer

A)  { -8} 
B)  { 8, -7, -2} 
C)  { -8, 7, 2} 
D)  { 8} 
A)  { -8} 
B)  { 8, -7, -2} 
C)  { -8, 7, 2} 
D)  { 8}

Question 11

Factor completely. If the polynomial cannot be factored, write prime.
-x2 - 5x - 24

Accepted Answer

A)  (x + 3)(x - 8) 
B)  (x - 3)(x + 1) 
C)  (x - 3)(x + 8) 
D)  Prime 
A)  (x + 3)(x - 8) 
B)  (x - 3)(x + 1) 
C)  (x - 3)(x + 8) 
D)  Prime

Question 12

Factor completely.
-  +   t +

Accepted Answer

A)    
B)    
C)      
D)  Prime 
A)    
B)    
C)      
D)  Prime

Question 13

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

Accepted Answer

A)  ( 4x + 5y)( 3x - 5y) 
B)  ( 4x + 5)( 3x - 5) 
C)  ( 12x + 5y)(x - 5y) 
D)  ( 4x - 5y)( 3x - 5y) 
A)  ( 4x + 5y)( 3x - 5y) 
B)  ( 4x + 5)( 3x - 5) 
C)  ( 12x + 5y)(x - 5y) 
D)  ( 4x - 5y)( 3x - 5y)

Question 14

Factor by grouping.
-4   + 3   + 3p   + 4   q

Accepted Answer

A)  (   +   )( 4p + 3q) 
B)  (p +   )( 3   + 4q) 
C)  (   +   )( 3p + 4q) 
D)  (   +   )( 3p - 4q) 
A)  (   +   )( 4p + 3q) 
B)  (p +   )( 3   + 4q) 
C)  (   +   )( 3p + 4q) 
D)  (   +   )( 3p - 4q)

Question 15

Factor completely. If the polynomial is prime, say so.
-256   - 81

Accepted Answer

A)  ( 4p + 3q)( 4p - 3q)( 16   + 9   ) 
B)    ( 4p - 3q) 
C)  ( 4p + 3q)( 4p + 3q)( 16   - 9   ) 
D)  ( 4p + 3q)( 4p - 3q)( 16   - 9   .) 
A)  ( 4p + 3q)( 4p - 3q)( 16   + 9   ) 
B)    ( 4p - 3q) 
C)  ( 4p + 3q)( 4p + 3q)( 16   - 9   ) 
D)  ( 4p + 3q)( 4p - 3q)( 16   - 9   .)

Question 16

Factor completely. If the polynomial cannot be factored, write prime.
-  - 14u + 48

Accepted Answer

A)  (u + 6)(u - 8) 
B)  (u - 6)(u - 8) 
C)  (u - 6)(u + 8) 
D)  (u + 6)(u + 8) 
A)  (u + 6)(u - 8) 
B)  (u - 6)(u - 8) 
C)  (u - 6)(u + 8) 
D)  (u + 6)(u + 8)

Question 17

Write the word or phrase that best completes each statement or answers the question.
-The binomial 16x2 + 64 is the sum of two squares that can be factored. Why is this possible?

Accepted Answer

16 is a factor of 64

Question 18

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-x2 + 4x - 21 = 0

Accepted Answer

A)  { 7, -3} 
B)  {-7, 1} 
C)  { 7, 3} 
D)  {-7, 3} 
A)  { 7, -3} 
B)  {-7, 1} 
C)  { 7, 3} 
D)  {-7, 3}

Question 19

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-x2 + 3x - 70 = 0

Accepted Answer

A)  { 10, -7} 
B)  {-10, 1} 
C)  {-10, 7} 
D)  { 10, 7} 
A)  { 10, -7} 
B)  {-10, 1} 
C)  {-10, 7} 
D)  { 10, 7}

Question 20

Factor completely.
-( 5m + n)   - 11( 5m + n)p + 28( 5m + n)

Accepted Answer

A)  ( 5m + n)(   - 11p + 28) 
B)  ( 5m + n)(p - 7)(p + 4) 
C)  ( 5m + n)(p - 7)(p - 4) 
D)  ( 5m + n)(p + 7)(p + 4) 
A)  ( 5m + n)(   - 11p + 28) 
B)  ( 5m + n)(p - 7)(p + 4) 
C)  ( 5m + n)(p - 7)(p - 4) 
D)  ( 5m + n)(p + 7)(p + 4)

Factor by grouping. -8x² + 14xt + 3t²

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -6x(x + 6) = (2x + 8)(x + 6)

Complete the factoring. - + 28 = 7 ( )

Find the pair of numbers whose product and sum are given. -Product: -45 Sum: -4

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -(x - 8)(x + 7) = 0

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Why is 5 called a triple solution to the equation (x - 5)³ = 0?

Factor completely. If the polynomial cannot be factored, write prime. -x² - x - 30

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -24p⁴ - 25p²= 10p³

Factor completely. -3x² - 3x - 18

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -(x + 8)( - 9x + 14) = 0

Factor completely. If the polynomial cannot be factored, write prime. -x² - 5x - 24

Factor completely. - + t +

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

Factor by grouping. -4 + 3 + 3p + 4 q

Factor completely. If the polynomial is prime, say so. -256 - 81

Factor completely. If the polynomial cannot be factored, write prime. - - 14u + 48

Write the word or phrase that best completes each statement or answers the question. -The binomial 16x² + 64 is the sum of two squares that can be factored. Why is this possible?

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -x² + 4x - 21 = 0

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -x² + 3x - 70 = 0

Factor completely. -( 5m + n) - 11( 5m + n)p + 28( 5m + n)

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

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Exam 7: Rational Expressions and Applications

Factor by grouping. -8x2 + 14xt + 3t2