Warm Up Math III 10/11/12Find the following using long division:

Remainder Theorem If a polynomial f(x) is divided by (x-r) and a

remainder of R is obtained, then f(r) = R.

Example: Use the remainder theorem to find the remainder of the following equation:

Since we are dividing by , we set x – 2 = 0 and solve. Therefore, x = 2.

Now, plug

Rational Root Theorem

If a polynomial has rational roots then p is a factor of and is a factor of

Rational Root Theorem

To find the possible roots of a polynomial:1. Find all factors of the leading coefficient (called

q)2. Find all factors of the last term, the one with no

variable (called p)3. Divided each p by each q.

Example: List all possible rational roots of