Essential Question: How do I divide polynomials?

1. How do I perform polynomial long division?

2. How do I perform polynomial synthetic division?

The following are our current tools for solving polynomials:

Factoring Most of the time the easiest, but only works with

rational zeros. Quadratic Formula

Works with all zeros, but can be a little messy. MUST USE for irrational & imaginary zeros.

Completing the Square Again, same as quadratic formula.

Graphing Can only get an approximate value of irrational

zeros, and can’t find imaginary zeros.

Is there another way to divide…of course!

Synthetic Division

When can we use synthetic division?

ONLY….when the divisor is a linear binomial with a leading coefficient of 1!!!! EX (x + 1)

We will take a look at synthetic division using linear binomials with coefficients other than one a little later…get excited!!

Use Synthetic Division to divide x4 – 10x2 – 2x + 4 by (x + 3)

-3 1 0 -10

-2 4

1

-3-3

9

-1

3

1

-31 remainde

r

3 2 13 1

3

x x x

x

Practice Problem

4 3(2x x 4) (x 1)

3 2 72x 3x 3x 3

x 1

You Try!!

3 2(x 3x 8x 5) (x 1)

2 1x 2x 6

x 1