Question 1

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-m( 4m - 23) = -15

Accepted Answer

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

Question 2

Factor completely.
-40m3n3-3m2n4-mn5

Accepted Answer

A)  mn3( 5m - n)( 8m + n)n3 
B)  mn3( 5m + n)( 8m - n) 
C)  mn3( 8m - n)( 5m + n) 
D)  n3( 5m - n)( 8m + n) 
A)  mn3( 5m - n)( 8m + n)n3 
B)  mn3( 5m + n)( 8m - n) 
C)  mn3( 8m - n)( 5m + n) 
D)  n3( 5m - n)( 8m + n)

Question 3

Solve the problem.
-The diagram below shows a rope connecting the top of a pole to the ground. The rope is 24 yd long and touches the ground 17 yd from the pole. How tall is the pole? Round approximations to the nearest tenth.
     
17 yd

Accepted Answer

A)  143.5 yd 
B)  8.5 yd 
C)  20.5 yd 
D)  16.9 yd 
A)  143.5 yd 
B)  8.5 yd 
C)  20.5 yd 
D)  16.9 yd

Question 4

Factor completely. If the polynomial is prime, say so.
-2x2 - 16x + 30

Accepted Answer

A)  2(x - 3)(x - 5) 
B)  2(x - 15)(x + 1) 
C)  Prime 
D)  ( 2x - 6)(x - 5) 
A)  2(x - 3)(x - 5) 
B)  2(x - 15)(x + 1) 
C)  Prime 
D)  ( 2x - 6)(x - 5)

Question 5

Factor the polynomial completely.
-125   + 216

Accepted Answer

A)  ( 125c + 6)(   - 30c + 36) 
B)  ( 5c - 6)( 25   + 30c + 36) 
C)  ( 5c + 6)( 25   + 36) 
D)  ( 5c + 6)( 25   - 30c + 36) 
A)  ( 125c + 6)(   - 30c + 36) 
B)  ( 5c - 6)( 25   + 30c + 36) 
C)  ( 5c + 6)( 25   + 36) 
D)  ( 5c + 6)( 25   - 30c + 36)

Question 6

Solve the problem.
-A triangle has a base of length 3x + 1 and a height of x + 6 and has an area of 45 square units. Find thebase and height. (A =   bh)

Accepted Answer

A)  base = 3 units; height = 15 units 
B)  base = 9 units; height = 5 units 
C)  base = 10 units; height = 9 units 
D)  base = 3 units; height = 30 units 
A)  base = 3 units; height = 15 units 
B)  base = 9 units; height = 5 units 
C)  base = 10 units; height = 9 units 
D)  base = 3 units; height = 30 units

Question 7

Choose the one alternative that best completes the statement or answers the question.Solve the equation.
-x(x - 3) = 18

Accepted Answer

A)  {-3, 6} 
B)  { 3, -6} 
C)  { 3, 6} 
D)  {-3, -6} 
A)  {-3, 6} 
B)  { 3, -6} 
C)  { 3, 6} 
D)  {-3, -6}

Question 8

Factor completely. If the polynomial cannot be factored, write prime.
-x2 - x - 40

Accepted Answer

A)  (x + 5)(x - 8) 
B)  (x - 40)(x + 1) 
C)  (x - 5)(x + 8) 
D)  Prime 
A)  (x + 5)(x - 8) 
B)  (x - 40)(x + 1) 
C)  (x - 5)(x + 8) 
D)  Prime

Question 9

Factor completely. If the polynomial is prime, say so.
-12   - 14y

Accepted Answer

A)  2y( 6y + 7) 
B)  y( 12y - 14) 
C)  2y( 6y - 7) 
D)  -2y( 6y + 7) 
A)  2y( 6y + 7) 
B)  y( 12y - 14) 
C)  2y( 6y - 7) 
D)  -2y( 6y + 7)

Question 10

Factor completely. If the polynomial cannot be factored, write prime.
-x2 + 39x + 40

Accepted Answer

A)  (x - 10)(x + 4) 
B)  (x + 40)(x - 1) 
C)  (x + 10)(x - 4) 
D)  Prime 
A)  (x - 10)(x + 4) 
B)  (x + 40)(x - 1) 
C)  (x + 10)(x - 4) 
D)  Prime

Question 11

Factor completely.
-4y4- 18y3+ 18y2

Accepted Answer

A)  y2( 2y - 3)(y - 3) 
B)  2y2( 2y - 3)(y + 3) 
C)  2y2( 2y + 3)(y - 3) 
D)  2y2( 2y - 3)(y - 3) 
A)  y2( 2y - 3)(y - 3) 
B)  2y2( 2y - 3)(y + 3) 
C)  2y2( 2y + 3)(y - 3) 
D)  2y2( 2y - 3)(y - 3)

Question 12

Factor by grouping.
-6y2 + 17y + 12

Accepted Answer

A)  ( 6y + 4)(y + 3) 
B)  ( 3y - 4)( 2y - 3) 
C)  ( 3y + 4)( 2y + 3) 
D)  Prime 
A)  ( 6y + 4)(y + 3) 
B)  ( 3y - 4)( 2y - 3) 
C)  ( 3y + 4)( 2y + 3) 
D)  Prime

Question 13

Factor completely. If the polynomial is prime, say so.
--2   + 28x - 98

Accepted Answer

A)  2   
B)  Prime 
C)  2   
D)  -2   
A)  2   
B)  Prime 
C)  2   
D)  -2

Question 14

Factor completely. If the polynomial cannot be factored, write prime.
-x2 + 5x - 50

Accepted Answer

A)  (x - 10)(x + 1) 
B)  (x + 10)(x - 5) 
C)  (x - 10)(x + 5) 
D)  Prime 
A)  (x - 10)(x + 1) 
B)  (x + 10)(x - 5) 
C)  (x - 10)(x + 5) 
D)  Prime

Question 15

Factor completely.
-18y2 + 81y - 45

Accepted Answer

A)  9(2y + 1)(y - 5) 
B)  ( 18y - 9)(y + 5) 
C)  Prime 
D)  9(2y - 1)(y + 5) 
A)  9(2y + 1)(y - 5) 
B)  ( 18y - 9)(y + 5) 
C)  Prime 
D)  9(2y - 1)(y + 5)

Question 16

Answer the question.
-What values of n will make xn a perfect square?

Accepted Answer

A)  n must be a multiple of 5. 
B)  n must be even. 
C)  n must be a power of 3. 
D)  n must be odd. 
A)  n must be a multiple of 5. 
B)  n must be even. 
C)  n must be a power of 3. 
D)  n must be odd.

Question 17

Choose the one alternative that best completes the statement or answers the question.
-Is x8y9z4 a common factor of x9y10z5and -x8y10z4?

Accepted Answer

A) True 
 B)False

Question 18

Factor completely.
-

Accepted Answer

A)    ( 2r - 3)( 2r - 1) 
B)    ( 2r - 3)( 2r + 1) 
C)    ( 4r - 3)(r + 1) 
D)    ( 2r + 3)( 2r - 1) 
A)    ( 2r - 3)( 2r - 1) 
B)    ( 2r - 3)( 2r + 1) 
C)    ( 4r - 3)(r + 1) 
D)    ( 2r + 3)( 2r - 1)

Question 19

Write the word or phrase that best completes each statement or answers the question. 
 
Provide an appropriate response.
-Give an example of three numbers whose greatest common factor is 10.

Accepted Answer

Answers va

Question 20

Write the word or phrase that best completes each statement or answers the question.
-Why is the answer (x2 - 225)(x2 + 225) not the correct answer to the instruction "Factor (x4 - 50,625) completely"?

Accepted Answer

The term x² - 225 can

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -m( 4m - 23) = -15

Factor completely. -40m³n³-3m²n⁴-mn⁵

Solve the problem. -The diagram below shows a rope connecting the top of a pole to the ground. The rope is 24 yd long and touches the ground 17 yd from the pole. How tall is the pole? Round approximations to the nearest tenth. 17 yd

Factor completely. If the polynomial is prime, say so. -2x² - 16x + 30

Factor the polynomial completely. -125 + 216

Solve the problem. -A triangle has a base of length 3x + 1 and a height of x + 6 and has an area of 45 square units. Find thebase and height. (A = bh)

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -x(x - 3) = 18

Factor completely. If the polynomial cannot be factored, write prime. -x² - x - 40

Factor completely. If the polynomial is prime, say so. -12 - 14y

Factor completely. If the polynomial cannot be factored, write prime. -x² + 39x + 40

Factor completely. -4y⁴- 18y³+ 18y²

Factor by grouping. -6y² + 17y + 12

Factor completely. If the polynomial is prime, say so. --2 + 28x - 98

Factor completely. If the polynomial cannot be factored, write prime. -x² + 5x - 50

Factor completely. -18y² + 81y - 45

Answer the question. -What values of n will make xⁿ a perfect square?

Choose the one alternative that best completes the statement or answers the question. -Is x⁸y⁹z⁴ a common factor of x⁹y¹⁰z⁵and -x⁸y¹⁰z⁴?

Factor completely. -

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Give an example of three numbers whose greatest common factor is 10.

Write the word or phrase that best completes each statement or answers the question. -Why is the answer (x² - 225)(x² + 225) not the correct answer to the instruction "Factor (x⁴ - 50,625) completely"?

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