# General Form of a Polynomial

A polynomial with one variable looks like this:

 example of a polynomial this one has 3 terms

But how de 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 ...

 ... for Degree 2 (Quadratic) we can use the letters a,b,c: ax2 + bx + c ... also Degree 3 (Cubic) can have letters: ax3 + bx2 + cx + d ... ... ... but for Degree "n", using 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):

So for the general case, we use this style:

And now we can say:

• an is the coefficient (the number you multiply by) for xn,
• an-1 is the coefficient for xn-1, etc,
• ... down to ...
• a1 which is the coefficient for x (because x1 = x), and
• a0 which is the constant term (because x0 = 1).

### Example: 9x4 + 5x2 - x + 7

• a4 = 9
• a3 = 0 (there is no x3 term)
• a2 = 5
• a1 = -1
• a0 = 7

Note also:

• The Degree of the polynomial is n
• an is not equal to zero (because then there would be no xn term)
• an is always a Real Number
• n can be 0, 1, 2, and so on (but not infinity)