Finding Zeros of Polynomials

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Zeros of Polynomials PolynomialType of Coefficient 5x 3 + 3x 2 + (2 + 4i) + icomplex 5x 3 + 3x 2 + √2x – πreal 5x 3 + 3x 2 + ½ x – ⅜rational 5x 3 + 3x.

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Presentation transcript:

Finding Zeros of Polynomials Honors Precalculus February 13-14, 2017 Mrs. Agnew

Essential Stuff Essential Question How do you find the zeros of a polynomial? Essential Vocabulary Zero Degree Rational Root Sythetic Division

Remainder & Factor Theorems The Remainder Theorem Given polynomial P(x), the value of P(c) is remainder from synthetic division using c. If you get a remainder of zero when using c in the “box,” what can you say about c? If c is a zero of function, then x – c is a factor of polynomial. Examples…

Rational Root Theorem Given a polynomial of degree n with integer coefficients, The Rational Root Theorem Potential zeros can be found by putting the factors of the constant term over the factors of the coefficient of the leading term. Use synthetic division to determine which potential zero is in fact a zero.

Zeros of Polynomials Steps to find the zeros of a polynomial: Find possible rational zeros (calculator) Use a rational zero and synthetic division to reduce polynomial Repeat until polynomial is reduced to quadratic Solve quadratic *A rational zero may be used more than once in synthetic division. Practice: pg 209 #40, 46, 68, 80, 96 ; pg 216 #34, 40

Homework: page 209 – 210 #41, 47, 49, 53, 55, 65, 69, 79, 81, 85, 95