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
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.
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.