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

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

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

Relative Minimum/Maximum Relative Maximum Relative Minimum

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

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

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

Rainbow Method Review

Factoring Example Factor

Finding the Zeros Example Find the zeros for

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

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