# Question About Long Division of Polynomials

• I
kyphysics
Dividend: 4x^3 - 6x - 11
Divisor: 2x - 4

In this problem above, the dividend lacks a variable to the second power, so we have to add a 0x^2 to make it:

4x^3 + 0x^2 - 6x - 11

Question:

Why do we add 0x^n? (n = missing powers)

In regular long division, we do no such thing. Why do we have to add these extra variables into the dividend in polynomial long division?

TVM!

## Answers and Replies

Mentor
2021 Award
I don't know. I don't.

Edit: It is probably to help perform the subtraction. If you don't add it you subtract from zero anyway. So writing it might help to avoid mistakes.

beamie564
Like the post above says, I think it's only to avoid error ( especially while learning it as a student). Wouldn't actually affect your answer in any way.

Mentor
You "add" 0, which means you do not change anything. In regular long division, the 0 would be there already to indicate the right places, in polynomials, you don't need to write +0x2 explicitely because every term has its meaning independent of where it is located.

Staff Emeritus
Homework Helper
Dividend: 4x^3 - 6x - 11
Divisor: 2x - 4

In this problem above, the dividend lacks a variable to the second power, so we have to add a 0x^2 to make it:

4x^3 + 0x^2 - 6x - 11

Question:

Why do we add 0x^n? (n = missing powers)

In regular long division, we do no such thing. Why do we have to add these extra variables into the dividend in polynomial long division?

TVM!
Sure we do. That's what zero is for.

If you want to do long division of 3065 by 42, the place value system we use to write decimal numerals is as follows:

3065 = 3 × 103 + 0 × 102 + 6 × 101 + 5 × 100

or

3065 = 3x3 + 0x2 + 6x + 5, where it is understood x = 10.

It's a similar situation when certain terms are missing from a polynomial dividend.

• jenniferAOI
kyphysics
Sure we do. That's what zero is for.

If you want to do long division of 3065 by 42, the place value system we use to write decimal numerals is as follows:

3065 = 3 × 103 + 0 × 102 + 6 × 101 + 5 × 100

or

3065 = 3x3 + 0x2 + 6x + 5, where it is understood x = 10.

It's a similar situation when certain terms are missing from a polynomial dividend.

Got it! Thanks.

jenniferAOI
Sure we do. That's what zero is for.

If you want to do long division of 3065 by 42, the place value system we use to write decimal numerals is as follows:

3065 = 3 × 103 + 0 × 102 + 6 × 101 + 5 × 100

or

3065 = 3x3 + 0x2 + 6x + 5, where it is understood x = 10.

It's a similar situation when certain terms are missing from a polynomial dividend.
wow. Did not see that either. thank you