Stitz-Zeager_College_Algebra_e-book

This has 3 variations in sign hence f has either 3

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: o see what happens. 1 2 4 −4 −11 12 −3 ↓ 2 −1 −6 3 1 4 −2 −12 60 2 ↓ 2 0 −6 √ 34 √0 −12 0 ↓ 43 12 √ √ −3 4 4 √3 0 ↓ −4 3 4 0 √ √ 2 This gives us 4x4 − 4x3 − 11x2 + 12x − 3 = x − 1 x− 3 x− − 3 2 with the constant in front 1 p(x) = 4 x − 2 2 x− √ 3 (4), or, when written √ x− − 3 We have shown that p is a product of its leading term times linear factors of the form (x − c) where c are zeros of p. It may surprise and delight the reader that, in theory, all polynomials can be reduced to this kind of factorization. We leave that discussion to Section 3.4, because the zeros may not be real numbers. Our final theorem in the section gives us an upper bound on the number of real zeros. Theorem 3.7. Suppose f is a polynomial of degree n, n ≥ 1. Then f has at most n real zeros, counting multiplicities. Theorem 3.7 is a consequence of the Factor Theorem and polynomial multiplication. Every zero c of f gives us a factor of the form (x − c) for...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online