Section 4.3 - f(-2) using synthetic division . The...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 4.3 Polynomial Division; The Remainder and Factor Theorems Recall, a factor divides an expression without a remainder. To see if x - 1 is a factor of x 4 - 1 divide x 4 - 1 by x - 1. If the remainder is zero then x - 1 is a factor of x 4 - 1. We may use polynomial long division or synthetic division. For both polynomial long division and synthetic division, add 0x k for any powers of x missing from the polynomial you are dividing. k is the missing power. Polynomial Long Division ( x 4 - 1 ) ÷ ( x - 1 ) = Is x - 5 a factor of x 3 - 9x 2 + 15 x + 25 ? Synthetic Divison ( x 4 - 1 ) ÷ ( x - 1 ) = Is x - 5 a factor of x 3 - 9x 2 + 15 x + 25 Remainder Theorem Let f(x) be a polynomial function. If f(x) is divided by x – c, then the remainder is equal to f(c). Given f(x ) = x 3 - 6x 2 + 11x - 6 . Find
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f(-2) using synthetic division . The remainder is so f(-2) = . Factor Theorem Let f(x) be a polynomial function. If f(c) = 0, then x -c is a factor of f(x). The remainder is f(c) so if the remainder is zero, then x -c is a factor of f(x). The factor theorem is useful in factoring polynomials to solve polynomial equations and find zeros of polynomial functions. Factor the polynomial function f(x). Then solve the equation f(x) = 0. f(x) = x 4-4x 3-7x 2 + 34x -24 The solutions to f(x) = 0 are the zeros of the polynomial f(x). Using synthetic division, determine whether 2 is a zero of f(x) = 3x 3 + 5x 2-6x + 18. Using synthetic division, determine whether -2i is a zero of g(x) x 3-4x 2 + 4x -16....
View Full Document

This note was uploaded on 10/12/2011 for the course MATH 1513 taught by Professor Staff during the Fall '08 term at Oklahoma State.

Page1 / 2

Section 4.3 - f(-2) using synthetic division . The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online