# I need to explain how to add/substract polynomials to my class. Could you help me with the correct steps ? Which examples /how should I organize it? I need to explain how to clasify polynomials by...

I need to explain how to add/substract polynomials to my class. Could you help me with the correct steps ? Which examples /how should I organize it?

I need to explain how to clasify polynomials by graph/degree/terms

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### 1 Answer

To **add** polunomials, I suggest the vertical method, that means set the two polynomial on top of each other, like we do in regular addtition.

The catch: you have to make sure that same degree monomial (or similar terms if more than one variable used) line up.

**Example **Add 3x^4-2x^2+5x-7 and -2x^4+9x^3+2x-11

3x^4 -2x^2 +5x -7

-2x^4+ 9x^3 +2x-11

x^4 + 9x^3 -2x^2 +7x -18

To **subtract** you can do the same just be careful not to forget that the subtraction change the sign of the term.

Example `3x-(-2x)=3x+2x=5x`

To classify your polynomial, you need to first understand how to classify a monomial.

Exampe: `3x^2` , is a second degree monominal. But `8x^2y^3` is a 5th degree monomial. We add the power of the variables only. So

`2^3x^4` is a 4th degree monomial not 7th.

Now when we look at the polynomial, we study the **degree** of each monomial, and the largest degree is the degree of your polynomial. Example: `3x^4-5x^2+7x` is a 4th **degree** polynomial. Its coeficient is called **leading coeficient**.

It is hard to classify every graph, but we can take a look at some basic polynomials with variable x

First degree polynomials also know as linear equations, are lines example y=2x+3

Second degree polynomials are called parabolas, they are your basic U shaped graph.