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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rcmath | High School Teacher | (Level 1) Associate Educator

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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.

 

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