Honors Algebra II with Trigonometry Mr. Agnew

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Presentation transcript:

Honors Algebra II with Trigonometry Mr. Agnew Polynomial Equations Honors Algebra II with Trigonometry Mr. Agnew

Essential Stuff Essential Question Essential Vocabulary How do you find the zeros of a polynomial function? Essential Vocabulary Polynomial Function Zeros or Root Rational Root Theorem Fundamental Theorem of Algebra

Solving Equations Methods to solve poly. equations: Graphing (x-intercepts) Factoring Rational Roots Drawbacks to using calculator?

Finding Roots… How can we find roots if polynomial does not factor? What are “rational numbers”? Numbers that can be written as a fraction. We have a method for identifying possible rational roots of any polynomial.

Rational Root Theorem Let p be all of the factors of the constant term (positive and negative). Let q be all of the factors of the leading coefficient (positive and negative). Then all possible rational roots are all factors of p over all factors of q.

Rational Root Theorem How does that help us find zeros or roots of a polynomial? These possible roots are numbers we can use with synthetic division… To bring polynomial down to quadratic And solve by factoring or Quad Formula Examples

Homework Homework 6.4: Rational Root Theorem

Algebra II with Trigonometry Mr. Agnew Polynomial Equations Algebra II with Trigonometry Mr. Agnew

Essential Stuff Essential Question Essential Vocabulary How do you find the zeros of a polynomial function? Essential Vocabulary Polynomial Function Zeros or Root Fundamental Theorem of Algebra

Fundamental Theorem Identify relationship between degree of polynomial and zeros. Fundamental Theorem of Algebra: A polynomial of degree n has exactly n roots, or zeros. Including all imaginary and multiple zeros.

Finding Zeros Steps for solving polynomial equation (or finding zeros of polynomial): Identify number of solutions/zeros Factor polynomial and solve if possible If not factorable, identify possible rational roots. Perform synthetic division to reduce polynomial to quadratic. Solve quadratic equation by factoring or using the quadratic equation

Using the Calculator When solving some problems, it is helpful to use the calculator to find zeros or maximum and minimum values. To do this, we will graph the function on our calculators and use the calculate menu. (2nd trace) Examples

Homework Homework 6.5: Solving Polynomials