Chapter 5.2 Evaluate & Graph Polynomial Functions #35 "In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann

Today we are going to… Look at Polynomials, and how to name them Evaluate by Synthetic Substitution And learn end behavior

Polynomials Term -Parts of an expression separated by a (+) or (-) sign. Monomial -Expression w/ only one term. Binomial -Expression w/ two terms. Trinomial -Expression w/ three terms. Polynomial - General name for expressions with at least two terms. Polynomials cannot have variables or negative numbers for powers.

Parts of a Polynomial Constant – Term w/o a variable Leading Coefficient – The coefficient of the term w/ the highest power. Degree of a Polynomial – The highest power in a polynomial. Standard Form - Polynomials should always be written w/ the highest power first and descending to the lowest power.

How to name a polynomial

There are two ways to evaluate You can use substitution-from algebra one ◦This is the plug in chug Or you can use synthetic substitution, NEW ◦Will become much quicker method than straight sub. Pulse you will be forced to use it later on in the chapter

Evaluate by Substitution Replace x with -2 & simplify

You try to Evaluate by Substitution Replace x with 3 & simplify

Evaluate by Synthetic Substitution

1. Label and Write all coefficients including any zeros inside the box. 2. Write the x-value on the outside of the box. 3. Bring down the leading coefficient. 4. Multiply the leading coefficient by the x- value. Write this number under the 2 nd coefficient. 5. Add these two numbers & continue the process.

Example 1. Write all coefficients including any zeros inside the box. 2. Write the x-value on the outside of the box. 3. Bring down the leading coefficient. 4. Multiply the leading coefficient by the x- value. Write this number under the 2 nd coefficient. 5. Add these two numbers & continue the process.

End Behavior of Polynomials Degree:Odd Leading Coeff: Positive Function goes up to the right and down to the left.

End Behavior of Polynomials Degree:Odd Leading Coeff: Negative Function goes down to the right and up to the left.

End Behavior of Polynomials Degree:Even Leading Coeff: Positive Function goes up to the right and up to the left.

End Behavior of Polynomials Degree:Even Leading Coeff: Negative Function goes down to the right and down to the left.

What's the end behavior?

Assignment p even