Math 41 Section 5.5

# Math 41 Section 5.5 - October 9 2007 5.5 The Real Zeros of...

This preview shows pages 1–3. Sign up to view the full content.

October 9, 2007 5.5 The Real Zeros of a Polynomial Function Use the Remainder Factor Theorems When we divide one polynomial (the dividend) by another (the divisor), we obtain a quotient polynomial and a remainder, the remainder being either the zero polynomial or a polynomial whose degree is less than the degree of the divisor. To check our work, we verify that (Quotient)(Divisor) + Remainder = Dividend This check routine is the basis for a famous theorem called the division algorithm for polynomials , which we state without proof. Division Algorithm for Polynomials If f(x) and g(x) denote polynomial functions and id 6(x) is not a zero polynomial, there are unique polynomial functions q(x) and r(x) such that where r(x) is either the zero polynomial or a polynomial of degree less than that of g(x) f(x) is the dividend g(x) is the divisor q(x) is the quotient Remainder theorem: Let f be a polynomial. Iff (x) is divided be x-c, then the remainder is f(c) Factor theorem: Let f be a polynomial function. Then x-c is a factor of f(x) iff f(c) = 0.

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

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern