a. Answer The GCF of the polynomial x 3 + y 3 ; x 2 + y 2 ; x + y are 1 . Explanation Given information: The given polynomials are x 3 + y 3 ; x 2 + y 2 ; x + y . Formula: Sum cube formula: x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) To Factorize x 3 + y 3 , Apply the sum cube formula: x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) ⇒ x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) The greatest common divisor of ( x + y ) ( x 2 − x y + y 2 ) , x 2 + y 2 and x + y are 1 . Therefore, the GCF of the polynomial x 3 + y 3 ; x 2 + y 2 ; x + y are 1 . b. To determine To Find: To find the LCM of the polynomials x 3 + y 3 ; x 2 + y 2 ; x + y . Answer The LCM of the polynomials x 3 + y 3 ; x 2 + y 2 ; x + y is ( x + y ) ( x 3 + y 3 ) ( x 2 + y 2 ) . Explanation Given information: The given polynomials are x 3 + y 3 ; x 2 + y 2 ; x + y . Formula: Sum cube formula: x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) To Factorize x 3 + y 3 , Apply the sum cube formula: x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) ⇒ x 3 + y 3 = ( x + y ) ( x 2 − x y + y 2 ) Compute an expression of factors that appears in at least one of the factored expressions ( x + y ) ( x 3 + y 3 ) ( x 2 + y 2 ) . Therefore, the LCM of the polynomials x 3 + y 3 ; x 2 + y 2 ; x + y is ( x + y ) ( x 3 + y 3 ) ( x 2 + y 2 ) .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 4.6, Problem 50WE

To determine

To Find:

To find the GCF of the polynomial x3+y3;x2+y2;x+y .

Expert Solution

Answer to Problem 50WE

The GCF of the polynomial x3+y3;x2+y2;x+y are 1 .

Explanation of Solution

Given information:

The given polynomials are x3+y3;x2+y2;x+y .

Formula:

Sum cube formula:

x3+y3=(x+y)(x2−xy+y2)

To Factorize x3+y3 ,

Apply the sum cube formula: x3+y3=(x+y)(x2−xy+y2)

⇒x3+y3=(x+y)(x2−xy+y2)

The greatest common divisor of (x+y)(x2−xy+y2) , x2+y2 and x+y are 1 .

Therefore, the GCF of the polynomial x3+y3;x2+y2;x+y are 1 .

To determine

To Find:

To find the LCM of the polynomials x3+y3;x2+y2;x+y .

Expert Solution

Answer to Problem 50WE

The LCM of the polynomials x3+y3;x2+y2;x+y is (x+y)(x3+y3)(x2+y2) .

Explanation of Solution

Given information:

The given polynomials are x3+y3;x2+y2;x+y .

Formula:

Sum cube formula:

x3+y3=(x+y)(x2−xy+y2)

To Factorize x3+y3 ,

Apply the sum cube formula: x3+y3=(x+y)(x2−xy+y2)

⇒x3+y3=(x+y)(x2−xy+y2)

Compute an expression of factors that appears in at least one of the factored expressions (x+y)(x3+y3)(x2+y2) .

Therefore, the LCM of the polynomials x3+y3;x2+y2;x+y is (x+y)(x3+y3)(x2+y2) .

Chapter 4.6, Problem 49WE

Chapter 4.6, Problem 51WE

Chapter 4 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 4.1 - Prob. 1OE Ch. 4.1 - Prob. 2OE Ch. 4.1 - Prob. 3OE Ch. 4.1 - Prob. 4OE Ch. 4.1 - Prob. 5OE Ch. 4.1 - Prob. 6OE Ch. 4.1 - Prob. 7OE Ch. 4.1 - Prob. 8OE Ch. 4.1 - Prob. 9OE Ch. 4.1 - Prob. 10OE

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To find the GCF of the polynomial x 3 + y 3 ; x 2 + y 2 ; x + y .

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To Find: To find the GCF of the polynomial x3+y3;x2+y2;x+y .

Answer to Problem 50WE

Explanation of Solution

To Find: To find the LCM of the polynomials x3+y3;x2+y2;x+y .

Answer to Problem 50WE

Explanation of Solution

Chapter 4 Solutions

Additional Math Textbook Solutions

To Find:

To find the GCF of the polynomial x3+y3;x2+y2;x+y .

To Find:

To find the LCM of the polynomials x3+y3;x2+y2;x+y .