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### Course: Algebra 2>Unit 4

Lesson 4: Polynomial Remainder Theorem

# Polynomial division: FAQ

## Why might we divide polynomials?

We divide polynomials for the same reason we divide numbers: to solve problems. By breaking a polynomial down into smaller, more manageable pieces, we can solve problems more easily.

## Why do we need to know how to divide quadratics specifically?

Quadratics are a very common type of polynomial, so they come up often in problems. Knowing how to divide them by linear factors (like $x$ or $x-2$) can help us factor them completely.

## How do we use the Polynomial Remainder Theorem?

The Polynomial Remainder Theorem tells us that if we divide a polynomial by a linear factor, the remainder will be equal to the polynomial evaluated at a certain value. So if we want to know what the remainder is when we divide a polynomial by $x-2$, we can just plug in $2$ to the polynomial and find out.

## Where do these topics come up in the real world?

Polynomials are used in a variety of disciplines, from engineering to physics to economics. Factoring polynomials allows us to work with them in a simpler form, which can make calculations and predictions easier.

## Want to join the conversation?

• Why might we multiply polynomials?
• I think it might be for the same reason we divide them: To solve problems
• Are there simpiler ways to divide polynomials?
• There is a way to divide polynomials called Synthetic Division. It makes dividing polynomials extremely easy! It takes a second to understand how to set it up but once you get it, it makes dividing polynomials easy work. I recommend watching a few videos on it!
• How am I supposed to know when to use a negative or a positive when plugging in (x-a)? Some problem explanations leave it as a negative but some switch it to a positive before solving it... why?
• Hi Bella, it is a simple sign change. If your divisor is (x-4) and you plug it into (x-a), you have (x-(-4)), or (x+4). If you plugged the divisor (x+4) into (x-a), the result would be (x-(4)), or (x-4).
• why do we have to know this
• how did 3x^2+1x-2 turn into (3x-2)(x+1)
• Here are the steps:

(3x-2)(x+1)
3x^2+3x-2x-2 <------ use FOIL
3x^2+x-2

That is how you can convert from factored to standard form. You can also just as easily do standard to factored form, but it's hard writing online w/o showing work.

Your question is a little irrelevant for this unit, as it is something you learn in Algebra 1. I'm not entirely sure, but after doing a quick search, units 13 and 14 in Algebra 1 may benefit you if you watch a couple of the videos for review. :)
• does the polynomial divisions have uses in calculus?
• Yep. There's a thing called "integration" which is pretty tedious to do for polynomial fractions. By using polynomial division, integration becomes much easier to do. Polynomial division also has uses beyond calculus, because it makes complicated polynomial fractions more manageable.
• when it's written like a polynomial over x, does that mean we have to use long division?
• If it’s just a polynomial divided by x, decrease the exponent by 1 on all the terms. Then, the remainder is the constant term if there is one.

Example: 5x^4-2x^3+9x+8 divided by x is 5x^3-2x^2+9 with a remainder of 8.