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### Course: Get ready for Precalculus>Unit 2

Lesson 8: Dividing quadratics by linear factors

# Intro to long division of polynomials

Any quotient of polynomials a(x)/b(x) can be written as q(x)+r(x)/b(x), where the degree of r(x) is less than the degree of b(x). For example, (x²-3x+5)/(x-1) can be written as x-2+3/(x-1). This latter form can be more useful for many problems that involve polynomials. The most common method for finding how to rewrite quotients like that is *polynomial long division*. 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)
• 37 times 2x would be 74x, right?
• Yes! When multiplying a constant by a variable term, multiply the constant by the coefficient of the variable.
(1 vote)
• 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!
• 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