Adding Polynomials

Date: 02/15/98 at 09:31:07
From: Sara
Subject: Adding polynomials

I don't know how to add polynomials. Can you please help me?

Date: 02/23/98 at 10:28:05
From: Doctor Jen
Subject: Re: Adding polynomials

Hi Sara,

When you're adding polynomials, the main thing to remember is to add
up terms of the same order. The exponents each variable has must match 
exactly or you can't add (or subtract) them. It's just like when you 
try to add x and y - you can't do it because they are different. 
x is different from x^2, so you can't add them together. Once you find 
that two things match, then you add them together.  

So this is what happens:

Let's say you want to add up  
      
      2(x^2) + 7x + 6 and 5(x^3) + 9(x^2) + 8x + 1.

(where x^2 is x to the power 2, and so on)

Start off by arranging them so that terms in x are in one column,
terms in x^2 are in another, terms in x^3.... like this:

First polynomial:            +  2(x^2) +  7x + 6
Second polynomial:    5(x^3) +  9(x^2) +  8x + 1

So, added together:   5(x^3) + 11(x^2) + 15x + 7

We leave 5(x^3) alone, because there are no other x^3 terms to add to 
it. Then we look at the x^2 terms - there are two of them, so we add 
the coefficients together (that's the number in front, remember). 
x^2 represents a thing of some sort (like saying x^2 represents an 
apple) - 2(x^2) represents two things and 9(x^2) represents nine more 
things. So all together you have eleven things. The same goes for the 
x term (that would be a thing of another sort, say a tennis ball) and 
the numbers at the end.

The same method will do for subtracting polynomials as well, only (big 
difference) take away instead of adding!

Just remember to keep different powers of x separate, and you'll be 
fine. I hope this helps you.

-Doctor Jen,  The Math Forum
Check out our web site http://mathforum.org/dr.math/