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### Course: Integrated math 3>Unit 3

Lesson 2: Dividing quadratics by linear factors

# Intro to long division of polynomials

Learn how to divide polynomials, also known as algebraic long division. This video starts with simple examples and gradually moves to more complex ones, demonstrating how to divide quadratics by linear factors. The process involves looking at the highest degree terms, dividing, and subtracting to simplify expressions. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• What about Synthetic Division? Is it something that recently came out? It is supposed to be shorthand version of Polynomial Division, where you just use the coefficient of each term and work it out that way. Look forward to your response!
• why is it that x goes 1 time in x square?
• if you don't see a number with an exponent, then it means the number's exponent is 1.
i.e 2 . you don't see any exponents but it has exponentof 1 because 2 is just 2..
• At , how come Sal can just ignore the 1 in the divisor, and only worry about the highest degree term? Shouldn't he be dividing x^2 with the whole divisor x+1?

I don't see how dividing x^2 only by the largest degree term x, and then multiplying the result into the divisor is the same thing as dividing x^2 with the entirety of (x+1).
"This solution will become crystal clear when you start dividing by higher polynomials.
Consider long division using the following notation:
17568 = 1*10^4 + 7*10*^3 + 5*10^2 + 6*10^1 + 8 & 10^0
Right?
Divide this by 202 which is 2*10^2 + 0*10^1 + 2
Take out the null coefficient and divide 17568 by 202 using powers of ten. You start by diving the largest power of ten into the largest power of ten and then multiplying everything by that number and subtracting. Try it, you'll like it."
• is sythentic division the same thing as dividing polynomials?
• It's a method of dividing a polynomial by a binomial so in some cases, yes
• Why should we only consider the largest power when dividing? For example at , he divides x^2 by x. Surely x^2/(x+1) is different from x^2/(x)
• I can't get my head around this for some reason, any tips?
• I couldn't either at first. I ended up watching the video a few more times and doing my own question from a textbook and then it clicked!
• 37 times 2x would be 74x, right?
• Yes, it’s right. You just need to multiply the constant
(1 vote)
• At , how does 2 go into 2x x times?
• He just means 2 times x equals 2x, just like 2 times 4 is 8, so just think of eight as 2x and 4 as x
• Why do you only consider the highest degree term in polynomial division it is not enough that it works please help as this is a fundamental part of mathematics which needs to be understood throughly and not just memorised
• It's just like long division of numbers.
___
When you divide 21 | 714 , you start with 7/2, not 7/21 or 7/2 and 7/1. In other words, you're sorting it into chunks biggest chunk first, then the next smaller, then the next smaller, and so on.
• is there such thing as a quad polynomial?
• A polynomial can have infinite length.