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### Course: Algebra 2>Unit 4

Lesson 4: Polynomial Remainder Theorem

# Intro to the Polynomial Remainder Theorem

The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. It tells us the remainder when a polynomial is divided by \[x - a\] is \[f(a)\]. This means if \[x - a\] is a factor of the polynomial, the remainder is zero. It's a neat trick to quickly find remainders without doing long division!

## Want to join the conversation?

• What is the difference between a binomial and a polynomial?
• binomial-they are with two terms
polynomial-monomial,binomial,trinomial everything are considered to be a polynomial
• why do i feel like him saying, "Starting polynomial long division is a good way to start your morning." Was a cry for help
• I can't relate...it's past midnight for me...
just squeezin' in some late-night studying :))
• When would it be useful to just calculate the remainder but not the quotient of polynomial division? Can anyone provide an example?
• Is the remainder theorem only true when you're dividing by x-a? Or is it true for x+a as well?
• It is true for x + a as well. x + a is another way of writing x - (-a). This comes into play when using synthetic division. Sometimes you'll be given a polynomial and a binomial in the form x + a. If it was x + 9, you would just take the opposite of 9, which is -9. Hope that helps.
• Shouldn't it be f(-a): You have x-1, and then you plug in 1. No?
• x-a! buddy a=1 so we plug in one!!
if it were x+a than you would be right buddie
• Does the polynomial remainder theorem also work on equations where the denominator 'x-a' where x has a coefficient or to anything greater than the 1st degree?
• It would work when x has a coefficient but when you have a denominator or divisor that has a degree that's greater than one, the remainder theorem wouldn't work as the remainder for higher degree terms is not constant.. (I got this from another person's answer on this website)
• What is the polynomial remainder theorem then?
• Can you use this Theorem when dividing a polynomial with x+a, with a being some positive constant?