Question

How would you describe a polynomial? how do you add and subtract polynomials?

Answer 1

A polynomial is any expression containing at least one variable and an addition or subtraction sign. The different parts are called terms, seperated by the aforementioned sign. For example, (x+2) has two terms, x and 2.
As for adding and subtracting, you look for terms of the same degree. That means that they have the same exponent. For example, you can add 2x and 7x together, but not 3x^3 and x^2. Once you've figured out the like terms, just add or subtract the coefficents.
Example problem: (3x+5+x^2)+(8x-2+x^3). 3x and 8x go together to give you 11x, 5 and -2 give you 3, and neither x^2 or x^3 has a like term, so they get left alone. Your answer would be (11x+3+x^2+x^3), but most teachers like it when you write them in descending order, so (x^3+x^2+11x+3).