Chapter 6-3 Dividing Polynomials (std Alg 2 3.0) Objectives: To understand long division of polynomials To understand synthetic division of polynomials.

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Presentation transcript:

Chapter 6-3 Dividing Polynomials (std Alg 2 3.0) Objectives: To understand long division of polynomials To understand synthetic division of polynomials To understand the Remainder Theorem and the Factor Theorem

Zeros of a Polynomial Function If P is a polynomial and c is a real number, then the following are true. 1.c is a zero of P. 2.x = c is a solution of the equation P(x) = 0. 3.x – c is a factor of P(x). 4.x = c is an x-intercept of the graph of P.

Ex 1.Factor

Ex 2. Find the zeros by factoring and ZPP a)P(x) = x 3 – 3x 2 – 10x

Ex 3. Divide by x – 4.

Ex 4. Use synthetic division to divide: by

Class Work Divide

Remainder Theroem If the polynomial P(x) is divided by x – c, then the remainder is the value P(c).

Ex 5. Use synthetic division and the Remainder Theorem to evaluate P(c).

Factor Theroem c is a zero of P if and only if x – c is a factor of P(x).

Ex 6. Use the Factor Theorem to show that x – c is a factor of P(x) for the given value of c and find all other zeros of P(x).

Class Work 3. Use synthetic division and the Remainder Theorem to evaluate P(c). 4. Use the Factor Theorem to show that x – c is a factor of P(x) for the given value of c and find all other zeros of P(x).

Ex 7. Find a polynomial of the specified degree that has the given zeros. degree 3; zeros -3, 0, and 1 Degree 3; zeros 1, 3, and 4