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Algebra II Section 5-4
I.
Objective: To divide polynomials using long & synthetic division.
II. Teacher activities:
A. Compare polynomial division to long division:
658 ÷ 31
(6 x2  5x  8)  (3x  1)
Rules for dividing polynomials by binomials:
1) Check for standard form
2) Check for missing terms – replace w/ 0 as the coefficient
3) Divide as if numbers
4) Place like terms over reach other
5) Write remainder over divisor & add to quotient
Use Polynomial long division:
6 x 2  11x  5
Ex 1
x 1
Synthetic Division – an efficient way to divide a polynomial by a linear
binomial in the form x – a
1. Check for standard form & missing terms
2. Write the coefficients with a in front (opposite of constant of divisor)
3. Bring lead coefficient down then multiply & add
Ex 2 Use synthetic division (2 x3  10 x2  9 x  15)  ( x  3)
x3  1
Ex 3 Use synthetic division
x 1
Remainder/Substitution Theorem – If P(x) is divided by x – a, P(a) is the
remainder.
Ex 4 Use synthetic division & the Remainder Theorem to find P(a).
P( x)  x5  2 x3  x2  2, a  3
III.
Assignment: p308: 9-29eoo, 31, 33-61eoo, 67-70all
Review packet over 5.1-5.4