1. Solving Polynomial Equations
Unit 1D Day 16

2. Do Now What is the difference between an expression and an equation?
Fill in the blank: The x-intercept of a graph is a point where _____ = _____.

3. Factoring Polynomials
Factoring means rewriting as a ___________.
Terms are factors of a polynomial if, when they are multiplied, they equal that polynomial:
Ex.: x2 + 2x – 15 =
_______ and ______ are factors of x2 + 2x – 15
In a polynomial equation, two polynomials are set equal to each other.

4. Zero Product Property
The only way a product can equal zero is if _______________________________
So the only way the polynomial can equal zero is _____________________________________

5. Steps for Solving Polynomial Equations
Solve for x: x2 + 2x = 15
Rearrange the terms to get zero on one side.
Tip: Try to keep your leading coefficient positive.
Factor.
Set each factor equal to zero and solve for x.

6. Solutions, Factors, Roots, Zeros
For our polynomial function: y = x2 + 2x – 15
The factors are: (x + 5) and (x - 3)
The roots/ solutions are: x = -5 and 3
The zeros/ x-intercepts are at: (-5, 0) and (3, 0)
A polynomial of degree n has at most _____ real zeros.
Ex: x2 + 2x – 15 is degree ______ and has ______ zeros.

7. Graph of a Polynomial Function
y = x2 + 2x – 15
The zeros of the polynomial are the values of x when the polynomial (y) equals zero.
These are also called the ______________