FST 11/9/16
Section 3.2
Name:
Warm Up:
WITHOUT a calculator, find each quotient.
1.
2.
Another method: Synthetic Division. Find the zero of the divisor and use it as the divisor in the synthetic
division. Use the coefficients of the dividend above the horizontal bar.
Example:
Uses of Synthetic division:
1. Remainder Theorem: If a polynomial p(x) is divided by (x – c), then the remainder is equal to p(c).
2. (x – c) is a factor of p(x) IFF p(c) = 0.
Example: Is (x + 2) a factor of
Example: Is (x – 4) a factor of
? If not, what is d(-2)?
? If not, what is c(4)?
Finding zeroes using the Rational Root Theorem: The Rational Root Theorem states if a rational number
,
where p and q have no common factors, is a root/zero of the equation, then p is a factor of the constant and q is
a factor of the leading coefficient.
What are all of the possible rational roots of

?
List the factors of 3 (3 is equal to p) and the factors of 4 (4 is equal to q).
Factors of p:
Factors of q:

The possible rational roots are of the form

Determine the roots/zeroes of the equation.
. List the possible rational roots.
Example:
What are the possible rational roots of
?
Determine the roots/zeroes of the equation.