Class Notes (839,506)
Canada (511,364)
Mathematics (870)
MATA30H3 (41)
Lecture

remainder theoram.docx

2 Pages
143 Views

Department
Mathematics
Course Code
MATA30H3
Professor
Ken Butler

This preview shows 80% of the first page. Sign up to view the full 2 pages of the document.
Description
Remainder Theorem  Long Division can be used to divide a polynomial by a binomial.  The result of the division of a polynomial function P(x) by a binomial of the form x – b can be written as P(x) = (x-b)Q(x) + R where Q(x) is the quotient and R is the remainder.  Division Statement: divisor x quotient + remainder = dividend  can be used to check the result of a division  Remainder theorem states that when a polynomial function P(x) is divided by x – b, the remainder is P(b), and when it is divided by ax-b, the remainder is P(b/a), where a and b are integers and a not = 0. Factor Theorem  For integer values of a and b, with a not equal 0,  Factor Theorem states that x – b is a factor of a polynomial P(x) if and only if P(b) = 0.  Similarly, if ax – b is a factor of P(x) if and only if P(b/a) = 0  Integral Zero Theorem states that if x – b is a factor of a polynomial function P(x) with leading coefficient 1 and remaining coefficients that are integers, then b is a factor of the constant term P(x).  Rational Zero Theorem states that if P(x) is a polynomial function with integer coefficients and x = b/a is a rational zero of P(x), then  b is a factor of the constant term of P(x)  a is a factor of the leading coefficient of P(x)  ax – b is a factor of P(x) Polynomial Equations  Real roots of a polynomial equation P(x) = 0 correspond to the x-intercepts of the graph of the polynomial function P(x).  X-intercepts of the graph
More Less
Unlock Document

Only 80% of the first page are available for preview. Some parts have been intentionally blurred.

Unlock Document
You're Reading a Preview

Unlock to view full version

Unlock Document

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit