# The blank in the following statements, How many terms does this polynomial have? List the terms: Which factor is common to each term? Factor the polynomial: 2 x 5 + 6 x 4 + 4 x 3 = ### 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 1E
To determine

## To fill: The blank in the following statements,How many terms does this polynomial have?                     List the terms:                     Which factor is common to each term?                 Factor the polynomial: 2x5+6x4+4x3=

Expert Solution

The complete statements are,

How many terms does this polynomial have?  3

List the terms:  2x5,6x4,4x3

Which factor is common to each term?  2x3

Factor the polynomial: 2x5+6x4+4x3=

2x3(x2+3x+2)

### Explanation of Solution

Given information:

The polynomial 2x5+6x4+4x3 .

Consider the provided polynomial 2x5+6x4+4x3 .

Number of terms in a polynomial is the number of terms separated by mathematical operations.

Here, the terms are separated by addition sign between three expressions, so, the given polynomial contains 3 terms.

The terms in the polynomial are the ones which are separated by addition sign between them,

So, the polynomial contains the following terms,  2x5,6x4,4x3  .

The greatest common factor to these terms is 2x3  .

Recall that to factorize a polynomial, take the common factor out and simplify it.

So, 2x5+6x4+4x3 will be factorized as,

2x5+6x4+4x3=2x3(x2+3x+2)

Thus, the complete statements are,

How many terms does this polynomial have?  3

List the terms:  2x5,6x4,4x3

Which factor is common to each term?  2x3

Factor the polynomial: 2x5+6x4+4x3=

2x3(x2+3x+2)

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