By Nat, Grade 11

Pre-Calculus

What is a rational number?

A rational zero is a solution to a polynomial that is rational.

What is a rational zero?

You can use the Rational Zero Test!

How do you find them?

The Rational Zero Test

Example 1 : Getting Started

To determine the actual real zeros of an equation, you must try out all the possible zeros and see if they yield a “0 (zero)” as an answer.

Determining the Actual Real Zeros

Example 2 : Moving On

Example 2 : Moving On

Example 2 : Moving On

Example 2 : Moving On

Example 2 : Moving On

Example 2 : Finishing

Extra Practice!

If the divisor of a synthetically divided equation is positive and every number in the last row is

positive, then this is the upper bound.

Example:

Bounds!!!

If the divisor of a synthetically divided equation is negative and the numbers in the last row

have alternating signs ( +, -), then this is the lower bound.

Example:

Bounds!!!

• Doyle, Matt. "Synthetic Division Solver." Matt Doyle :: Welcome. Web. 11 Dec. 2011. <http://www.mattdoyle.net/old/synthetic.html>.

• Hungerford, Thomas W., Irene Jovell, and Betty Mayberry. "Chapter 4: Polynomial and Rational Functions." Precalculus: a Graphing Approach. Austin: Holt, Rinehart and Winston, 2006. Print.

• Mr. Scott O’Brady’s Lectures (Precalculus)

Bibliography

For watching!!!