2.3 Real Zeros of Polynomial Functions-Synthetic and Long Division Blog

In section 2.3 we look at different ways to divide polynomials. The two major ways we do this is by long division of polynomials and synthetic division.

When doing long division of polynomials you treat the problem just as you would when doing a long division problem with simple numbers

Solve the polynomial just as you would this:

Another way to divide polynomials in Synthetic Division!

This is a nice shortcut for long division. It is a pattern. Vertically you must add the terms. And your diagonal patter is to multiply by the factor outside.

In synthetic division if the integers add up to 0, (X-1) is a factor.

The Rational Zero Test
The Rational Zero Test relates the possible rational zeros of a polynomial to the leading coefficient and to the constant term of the polynomial.
 Possible rational zeros=  (factors of constant term)/(factors of leading coefficient)