5-3 Dividing PolynomialsObjectivesStudents will be able to:1) Divide polynomials using long division2) Divide polynomials using synthetic division

Example 1: Polynomial/Monomial

Ex 1B: Polynomial/MonomialSimplify.

Ex 1C: Polynomial/MonomialSimplify.

Apply Concepts1: Simplify!

1. 2.

Remember Long Division?

Polynomial Long Division

1) Rewrite the problem in long division form (if not already done).

2) In each polynomial, line the terms up in descending order, with respect to their degree.

3) Within the numerator (dividend), if a degree term is missing, add it in with a 0 coefficient.

Example: is missing the second degree term, so add it in.

Ex 2:Division Algorithm

6(z – 4) = 6z – 24

Ex 2B: Division

Ex 2C: Division

Ex 2D: Division

Ex 3: Quotient With RemaindersSimplify:

Ex 3B: Remainders

Ex 3C: Remainders

Synthetic DivisionSynthetic division: method of polynomial

long division using only the coefficients of the terms

In order to use synthetic division, the denominator (divisor) must be a first degree binomial, which takes on the form

Also, the coefficient on the first degree term of the divisor must be a 1.

Let’s examine the steps of synthetic division while working through a problem.

Synthetic Division

Synthetic Division

Ex 4:Synthetic Division

Ex 4B: Synthetic Division