Solving Polynomial Equations Unit 1D Day 16

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 _____ = _____.

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.

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

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.

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.

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 ______________