# The degree of polynomial when two polynomials are multiplied. ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 133E

(a)

To determine

## To explain: The degree of polynomial when two polynomials are multiplied.

Expert Solution

When are polynomials are multiplied degrees are added up.

### Explanation of Solution

Given information:

The two polynomials.

Formula used:

The law of exponent anam=an+m .

When polynomials are multiplied the degree of the product polynomial is the sum of the degree.

In the resultant polynomial the leading power of both the terms will emerge.

Consider two polynomials say (x2+x+3) and (x1) .

Now, product of the above two polynomials is,

(x2+x+3)(x1)=x3x2+x2x+3x3=x3+2x3

Thus, when are polynomials are multiplied degrees are added up.

(b)

To determine

### To explain: The degree of polynomial when two polynomials are added.

Expert Solution

When polynomials are added degree is at most the largest of the degrees.

### Explanation of Solution

Given information:

The two polynomials.

When polynomials are added the degree is at most the largest of the degrees.

In the resultant polynomial it is not necessary that leading power of both the terms will emerge.

Consider two polynomials say (x2+x+3) and (x1) .

Now, add the above two polynomials,

(x2+x+3)+(x1)=x2+x+3+x1=x2+2x+2

Thus, polynomials are added degree is at most the largest of the degrees.

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