1. Role of Zero in Factoring
Eureka Math Algebra 2 Module 1 Lesson 11

2. Objective
Students find solutions to polynomial equations where the polynomial expression is not factored into linear factors.
Students construct a polynomial function that has a specified set of zeros with stated multiplicity.
Standards
A.APR.B.3

3. 2 hints if you need them Hint 1: the problem uses the zero product property: if ab=0, then a=0 or b=0. Hint 2: Try to factor each quadratic separately.
The solutions are x = -2, -3, 4, or -1

4. (x+3) (x-3) (x+4) (x-4) = 0 The answers are x = -3, 3, -4, or 4

5. Since we know (x-1) is a factor of the polynomial, we can divide to find the quadratic polynomial.
We also know that the quadratic polynomial 4x ²-8x-5 has linear factors of (2x+1) and (2x-5)

6. This is the graph of our function in example 1.
The Multiplicity of a polynomial is how many times a particular number is a zero for a given polynomial. 
So for our graph the zero 1, 5/2, and -1 has a multiplicity of 1.

9. If p is a polynomial function of degree n, then the sum of the multiplicities of all of the zeros is less than or equal to n. If p can be factored into linear terms, then the sum of the multiplicities of all of the zeros is exactly equal to n.