# To choose the appropriate description of polynomial end behavior

### 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 3.2, Problem 2E

a

To determine

## To choose the appropriate description of polynomial end behavior

Expert Solution

The end behavior of polynomial is y+ as x  and y as  x

### Explanation of Solution

Given information:

y=x38x2+2x15

End behavior of the polynomial depends on the leading coefficient of the polynomial and degree of polynomial.

When the degree of polynomial is odd:

If leading co efficient is positive then y+ as x and y as  x

If leading co efficient is negative then y as x and y+ as  x

When the degree of polynomial is even:

If leading co efficient is positive then y+ as x and y+ as  x

If leading co efficient is negative then y as x and y as  x

Therefore the leading co efficient is positive odd number 1 and .

Hence , the end behavior of polynomial is,

y+ as x and y as  x

b

To determine

### To choose the appropriate description of polynomial end behavior

Expert Solution

The end behavior of polynomial is y as x and y+ as  x

### Explanation of Solution

Given information:

y=2x4+12x+100

End behavior of the polynomial depends on the leading coefficient of the polynomial and degree of polynomial.

When the degree of polynomial is odd:

If leading co efficient is positive then y+ as x and y as  x

If leading co efficient is negative then y as x and y+ as  x

When the degree of polynomial is even:

If leading co efficient is positive then y+ as x and y+ as  x

If leading co efficient is negative then y as x and y as  x

Therefore the leading co efficient is negative even 2 .

Hence , the end behavior of polynomial is

y as x and y+ as  x

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