Associated Topics || Dr. Math Home || Search Dr. Math

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

Date: 02/23/98 at 10:28:05
From: Doctor Jen

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

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/

Associated Topics:
High School Polynomials

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search