1. Polynomials, Linear Factors, Zeros1
Definitions 2
Relative Minimum/Maximum 3
Factors & Zeros

2. Definitions Factor Zeros Multiplicity of zeros
Each term in the completely factored form of a polynomial
Can have repeated factors
Zeros
Values found when each factor is set equal to zero and solved
Also called the x-intercepts or roots
Multiplicity of zeros
The number of times a root is repeated
i.e. (x-2)2 = (x-2)(x-2), so the solution is x=2 and x=2

3. Definitions Relative minimum Relative Maximum
The value of a function at a down-to-up turning point
Relative Maximum
The value of a function at a up-to-down turning point

4. Relative Minimum/Maximum
Relative Maximum
Relative Minimum

5. Relative Minimum/Maximum
Degree = 3
3-1=2

6. Finding the Zeros from a Polynomial
Write the polynomial in standard form
Set the polynomial equal to zero
Factor using GCF
Factor using “Rainbow Method” or Special Rules
Set each factor equal to zero
Solve each factor

7. GCF Review
Look for the largest common number and/or variables in each term
Divide each term by the common terms

8. Rainbow Method Review

9. Factoring Example
Factor

10. Finding the Zeros Example
Find the zeros for

11. Writing a Polynomial from the Zeros
Substitute each zero (root) for a in (x-a)
Multiply the (x-a)’s together
Combine like terms

12. Writing a Polynomial from Zeros Example
What polynomial function in standard form has zeros -2, 2, and 3?