General Form of a Polynomial

A polynomial with one variable looks like this:

polynomial example
example of a polynomial
this one has 3 terms

But how do we talk about general polynomials? Ones that may have lots of terms?

General Form

A general polynomial (of one variable) could have any number of terms:

Degree 2 (Quadratic) can have letters a,b,c:ax2 + bx + c
Degree 3 (Cubic) can have letters a,b,c,d:ax3 + bx2 + cx + d
But for Degree "n" letters won't work:axn + bxn-1 + ... + ?x + ?

The trouble is, we don't know what letters to end on!

So instead of "a, b, c, ..." we use the letter "a" with a little number next to it, which says which term it belongs to: polynomial general term

So for the general case, we use this style:

polynomial general form

And now we can say:

Example: 9x4 + 5x2 - x + 7

Note also: