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Polynomials, Linear Factors, Zeros

Polynomials, Linear Factors, Zeros. 1. Definitions. 2. Relative Minimum/Maximum. 3. Factors & Zeros. Definitions. Factor Each term in the completely factored form of a polynomial Can have r epeated factors Zeros Values found when each factor is set equal to zero and solved

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Polynomials, Linear Factors, Zeros

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

  2. Definitions • Factor • 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 • 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?

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