Polynomials are things like 2x2 −
3x + x3 − 3. There are three basic
questions you can be asked about a polynomial. (There are lots of
other harder questions, too, but we'll start with these.)
- The number of terms is just the number of pieces
separated by plus or minus signs. So, in our example,
2x2 is one term, 3x is a second
term, x3 is a third term and 3 is a fourth
term. So there are 4 terms.
- The degree means the biggest exponent
of x. (Of course, it could be some other letter
besides x.) Here that's 3. But there are two special
cases to remember. First, if x is never raised to a
power, then the degree is 1. (Then it's a linear function, like
the ones in earlier sections.) Second, if x doesn't
appear at all (that is all we have is a number, like
−3), then the degree is 0.
- The leading coefficient means the number in front of
whatever term the degree came from. In this case, the degree
came from the term x3, which is the same as
1x3, so the leading coefficient is 1. If
there's a minus sign in front of that term, then it counts as
part of the leading coefficient.