We covered polynomials plenty of times in the past, so we only need a little time to refresh ourselves on the basics. Prepare yourself, Shmooper, for a quick-time polynomial review.
• What do they look like? They're a bunch of variables with exponents, with constants attached. But, they have no fractional or negative exponents, just whole numbers. Polynomials keep it simple up top.
• The degree is the highest-numbered exponent around. When it's even, the polynomial throws its arms up in the air like it just don't care. Or down to the ground, they do that too. Odd polynomials have one arm up and one down.
• Polynomials are like trees, because they have roots. These roots are the x values where the polynomial equals 0. Trees don't have those.
• If we look at its graph, a polynomial will have no breaks, gaps, washouts, or bald spots. Polynomial functions also obey all the rules of functions, such as the vertical-line test.
• Polynomials can be added, subtracted, multiplied, and divided. That's the whole shebang.
Okay, that was fast. Have we set a new Shmoop record?