If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Class 9 (Foundation)

### Course: Class 9 (Foundation)>Unit 5

Lesson 2: Dividing polynomials

# Divide polynomials by monomials (with remainders)

Sal divides (7x^6+x^3+2x+1) by X^2, and writes the solution as q(x)+r(x)/x^2, where the degree of the remainder, r(x), is less than the degree of x^2. Created by Sal Khan.

## Want to join the conversation?

• Can someone tell me the parts of a polynomial like : degree (etc)
• Degree is the highest exponent a variable is raised to in a given function. Take the function:
f(x) = x^3 + x^2 + x + 5
3 is the degree.
The variable is x (self-explanatory).
The constant term is 5 (basically the coefficient of the x^0 term).
• im having trouble I need help
• In this video professor Sal is explaining how to divide polynomials by monomials with reminders i.e.,
(4x^2+2x^2+x+1)/x^2 [my own example]
for this {(4x^2/x^2),(2x^2/x^2),[(x+1)/x^2]}
"[(x+1)/x^2]}" this is because as in question they have asked to answer in the format - "q(x)+r(x)/x^2, where the degree of the remainder, r(x), is less than the degree of x^2"
Hope it helps
• How are you getting 7xto the 6th power to 7x to the 4th power? I'm not understanding this at all...
• I looked in multiple places to find polynomial division with binomial's and remainders, but I couldn't find it anywhere, could someone please direct me to where to find this if it exists, and if not could someone tell me in full description what to do? I would be very grateful,

Many Thanks.
• Why can't we use long division to solve this problem? And when do I know to use long division, or (this type) of division? Thanks in advance!
(1 vote)
• This question was answered before:
` why not use long division? `
"Since this is a monomial we are dividing by, it is straightforward enough to do directly. It certainly is possible to do it long division style."
• Isn't the remainder of the division supposed to be 2x-1 instead of 2x+1?
Why did sal write 2x+1/x^2 instead of 2x-1/x^2
(1 vote)
• No. The remainder is indeed 2x+1. You get to that remainder as Sal did, or you can perform a long division to be sure. But in both cases the remainder is 2x+1.
• x square + 3x square+3x +1 / x + pi. remainder equals to?
(1 vote)
• 4pi^2-3pi+1. And the quotient will be 4x-4pi+3.

Or you made a mistake and actually meant for the first term in the numerator to be cubed. In that case, you get the remainder -pi^3+3pi^2-3pi+1 and the quotient x^2-xpi+3x+pi^2-3pi+3. If you look carefully at the remainder, it can be simplified to -(pi-1)^3

On both cases, as far as performing a division to simplify the expression goes, you are better of by just leaving the original expression untouched.

Also a note:
I reached both results above by performing a long division and double checking my results. The process may seem daunting at first, but you really just need to look at pi as if it was just another variable. Essentially performing long division as if you were dividing polynomials with xy terms. You just look at pi as being your y.