Question 1

Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. n3 + 4n2 - 9n - 36, n + 3

Accepted Answer

A)  (n + 3)(n2 - 7n - 12) 
B)  (n + 3)(n + 3)(n - 4) 
C)  (n + 3)(n2 + n - 12) 
D)  (n + 3)(n - 3)(n + 4) 
A)  (n + 3)(n2 - 7n - 12) 
B)  (n + 3)(n + 3)(n - 4) 
C)  (n + 3)(n2 + n - 12) 
D)  (n + 3)(n - 3)(n + 4) D

Question 2

Factor completely. 8w3x - 800wx

Accepted Answer

A)  The expression is prime. 
B)  8wx(w - 10)(w + 10) 
C)  8wx(w - 10)2 
D)  8wx(w2 - 102) 
A)  The expression is prime. 
B)  8wx(w - 10)(w + 10) 
C)  8wx(w - 10)2 
D)  8wx(w2 - 102) B

Question 3

Factor out the greatest common factor. (m - 4)8 + (m - 4)m

Accepted Answer

A)  The polynomial is prime. 
B)  m2 + 4m - 32 
C)  (m - 4)8 + m 
D)  (m - 4)(8 + m) 
A)  The polynomial is prime. 
B)  m2 + 4m - 32 
C)  (m - 4)8 + m 
D)  (m - 4)(8 + m) D

Question 4

Factor the given polynomial completely. c4 + d4

Accepted Answer

A)  c2d2(c2 - d2) 
B)  (c - d)2(c + d)2 
C)  The polynomial is prime. 
D)  (c - d)(c + d)(c2 + d2) 
A)  c2d2(c2 - d2) 
B)  (c - d)2(c + d)2 
C)  The polynomial is prime. 
D)  (c - d)(c + d)(c2 + d2)

Question 5

Factor the given polynomial completely. 6v2w - 48vw + 90w

Accepted Answer

A)  w(6v - 30)(6v - 18) 
B)  6w(v - 5)(v - 3) 
C)  The polynomial is prime. 
D)  6w(v2 - 8v + 15) 
A)  w(6v - 30)(6v - 18) 
B)  6w(v - 5)(v - 3) 
C)  The polynomial is prime. 
D)  6w(v2 - 8v + 15)

Question 6

Solve the equation.

Accepted Answer

A)  1, 5 
B)    
C)    
D)    
A)  1, 5 
B)    
C)    
D)

Question 7

Find the greatest common factor of the given terms. 6wx, 14xy, 10wy

Accepted Answer

A)  2wx 
B)  1 
C)  2wxy 
D)  2 
A)  2wx 
B)  1 
C)  2wxy 
D)  2

Question 8

Find the prime factorization. 88

Accepted Answer

A)  8·11 
B)  22·3·11 
C)  23·11 
D)  2·44 
A)  8·11 
B)  22·3·11 
C)  23·11 
D)  2·44

Question 9

Factor the given polynomial completely. If the polynomial is prime, say so. 5r2 + 34r + 45

Accepted Answer

A)  (5r - 9)(r + 5) 
B)  (5r - 9)(r - 5) 
C)  The polynomial is prime. 
D)  (5r + 9)(r + 5) 
A)  (5r - 9)(r + 5) 
B)  (5r - 9)(r - 5) 
C)  The polynomial is prime. 
D)  (5r + 9)(r + 5)

Question 10

Factor. 125x3 - 27

Accepted Answer

A)  (5x - 3)(25x2 - 15x + 9) 
B)  (5x + 3)(25x2 - 30x + 9) 
C)  (5x + 3)(25x2 - 15x + 9) 
D)  (5x - 3)(25x2 + 15x + 9) 
A)  (5x - 3)(25x2 - 15x + 9) 
B)  (5x + 3)(25x2 - 30x + 9) 
C)  (5x + 3)(25x2 - 15x + 9) 
D)  (5x - 3)(25x2 + 15x + 9)

Question 11

Factor. 16r2 - 25

Accepted Answer

A)  The expression is prime. 
B)  (4r - 5)2 
C)  (4r - 5)(4r + 5) 
D)  (16r - 5)(16r + 5) 
A)  The expression is prime. 
B)  (4r - 5)2 
C)  (4r - 5)(4r + 5) 
D)  (16r - 5)(16r + 5)

Question 12

Factor the given polynomial completely. If the polynomial is prime, say so. x3 + xy + 2x2 + 2y

Accepted Answer

A)  The polynomial is prime. 
B)  (x + 2)(x2 + y) 
C)  (x + 2)(x + y) 
D)  (x2 + 2)(x + y) 
A)  The polynomial is prime. 
B)  (x + 2)(x2 + y) 
C)  (x + 2)(x + y) 
D)  (x2 + 2)(x + y)

Question 13

Factor out the opposite of the greatest common factor. 35y3 - 7y2

Accepted Answer

A)  -7y2(5y - 1) 
B)  -7y2(-5y + 7) 
C)  -7y2(-5y + 1) 
D)  -y2(35y - 7) 
A)  -7y2(5y - 1) 
B)  -7y2(-5y + 7) 
C)  -7y2(-5y + 1) 
D)  -y2(35y - 7)

Question 14

Factor. vw - 9w - 2v + 18

Accepted Answer

A)  (v - 9)(w - 2) 
B)  The expression is prime. 
C)  (v + 9)(w + 2) 
D)  (v - 2)(w - 9) 
A)  (v - 9)(w - 2) 
B)  The expression is prime. 
C)  (v + 9)(w + 2) 
D)  (v - 2)(w - 9)

Question 15

Solve the given equation. v3 - 3v2 - 13v + 15 = 0

Accepted Answer

A)  -3, 1, 5 
B)  3, -1 
C)  1, 5 
D)  3, 1, -5 
A)  -3, 1, 5 
B)  3, -1 
C)  1, 5 
D)  3, 1, -5

Question 16

Find the greatest common factor for the given numbers. 9, 48

Accepted Answer

A)  6 
B)  9 
C)  1 
D)  3 
A)  6 
B)  9 
C)  1 
D)  3

Question 17

Factor out the greatest common factor. 81s2t2 - 63s2t + 54st2

Accepted Answer

A)  -9s2t2(-9st + 7s - 6t) 
B)  st(81st - 63s + 54t) 
C)  The polynomial is prime. 
D)  -9st(-9st + 7s - 6t) 
A)  -9s2t2(-9st + 7s - 6t) 
B)  st(81st - 63s + 54t) 
C)  The polynomial is prime. 
D)  -9st(-9st + 7s - 6t)

Question 18

Factor. qrs - 5q - 6rs + 30

Accepted Answer

A)  (q - 6)(rs - 5) 
B)  (q + 6)(rs - 5) 
C)  The expression is prime. 
D)  (q - 5)(rs - 6) 
A)  (q - 6)(rs - 5) 
B)  (q + 6)(rs - 5) 
C)  The expression is prime. 
D)  (q - 5)(rs - 6)

Question 19

Factor the given polynomial completely. If the polynomial is prime, say so. w2 - 8w

Accepted Answer

A)  The polynomial is prime. 
B)  w(w - 8) 
C)  w(w2 - 8w) 
D)  (w - 8)(w + 8) 
A)  The polynomial is prime. 
B)  w(w - 8) 
C)  w(w2 - 8w) 
D)  (w - 8)(w + 8)

Question 20

Factor. 36u2 - 12u + 1

Accepted Answer

A)  The expression is prime. 
B)  (6u - 1)2 
C)  (6u - 1)(6u + 1) 
D)  (6u + 1)2 
A)  The expression is prime. 
B)  (6u - 1)2 
C)  (6u - 1)(6u + 1) 
D)  (6u + 1)2

Exam 5: Section 1: Factoring

Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. n3 + 4n2 - 9n - 36, n + 3

Factor completely. 8w3x - 800wx

Factor out the greatest common factor. (m - 4)8 + (m - 4)m

Factor the given polynomial completely. c4 + d4

Factor the given polynomial completely. 6v2w - 48vw + 90w

Solve the equation.

Find the greatest common factor of the given terms. 6wx, 14xy, 10wy

Find the prime factorization. 88

Factor the given polynomial completely. If the polynomial is prime, say so. 5r2 + 34r + 45

Factor. 125x3 - 27

Factor. 16r2 - 25

Factor the given polynomial completely. If the polynomial is prime, say so. x3 + xy + 2x2 + 2y

Factor out the opposite of the greatest common factor. 35y3 - 7y2

Factor. vw - 9w - 2v + 18

Solve the given equation. v3 - 3v2 - 13v + 15 = 0

Find the greatest common factor for the given numbers. 9, 48

Factor out the greatest common factor. 81s2t2 - 63s2t + 54st2

Factor. qrs - 5q - 6rs + 30

Factor the given polynomial completely. If the polynomial is prime, say so. w2 - 8w

Factor. 36u2 - 12u + 1

Section 1: Real Numbers and Their Properties

Section 2: Real Numbers and Their Properties

Section 1: Linear Equations and Inequalities in One Variable

Section 2: Linear Equations and Inequalities in One Variable

Section 1: Linear Equations and Inequalities in Two Variables

Section 2: Linear Equations and Inequalities in Two Variables

Section 1: Exponents and Polynomials

Section 2: Exponents and Polynomials

Section 2: Factoring

Section 1: Rational Expressions

Section 2: Rational Expressions

Section 1: Systems of Linear Equations

Section 2: Systems of Linear Equations

Section 1: More on Inequalities

Section 2: More on Inequalities

Section 1: Radicals and Rational Exponents

Section 2: Radicals and Rational Exponents

Section 1: Quadratic Equations and Inequalities

Section 2: Quadratic Equations and Inequalities

Section 1: Functions

Section 2: Functions

Section 1: Exponential and Logarithmic Functions

Section 2: Exponential and Logarithmic Functions

Section 1: Nonlinear Systems and the Conic Sections

Section 2: Nonlinear Systems and the Conic Sections

Section 1: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Section 2: Sequences and Series Available Online at Www.mhhe.com/dugopolski

Mathematical Problem Set

Algebraic Equations and Problem Solving

Algebra and Math Problems

Algebraic Equation Practice

Filters

Factor the polynomial below completely, given that the binomial following it is a factor of the polynomial. n³ + 4n² - 9n - 36, n + 3

Factor completely. 8w³x - 800wx

Factor the given polynomial completely. c⁴+ d⁴

Factor the given polynomial completely. 6v²w - 48vw + 90w

Factor the given polynomial completely. If the polynomial is prime, say so. 5r² + 34r + 45

Factor. 125x³ - 27

Factor. 16r² - 25

Factor the given polynomial completely. If the polynomial is prime, say so. x³+ xy + 2x² + 2y

Factor out the opposite of the greatest common factor. 35y³ - 7y²

Solve the given equation. v³ - 3v² - 13v + 15 = 0

Factor out the greatest common factor. 81s²t² - 63s²t + 54st²

Factor the given polynomial completely. If the polynomial is prime, say so. w² - 8w

Factor. 36u² - 12u + 1