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### Course: Integrated math 3>Unit 3

Lesson 2: Dividing quadratics by linear factors

# Dividing quadratics by linear expressions (no remainders)

We can divide polynomials similarly to how we divide integers. For example, when we divide (x²+7x+10) by (x+2), we are asking "what can we multiply by (x+2) to get (x²+7x+10)?" We can answer this question in many ways. One is with using factorization, and another one is long division.

## Want to join the conversation?

• I was wondering if Khan Academy had a video on the foil method. It is confusing me.
Thanks
• FOIL is a method for multiplying binomials. It stands for First Outside Inside Last.

For example:
(x+1)(x+1)
= (x)(x) [First] + (x)(1) [Outside] + (1)(x) [Inside] + (1)(1) [Last]
= x^2+2x+1
• Did anyone else notice he spelled Khan wrong at ?
• Correct, but Sal did not spell anything wrong, it was Youtube. They auto generate those based on the sound, so people who cannot hear, will be able to watch his videos, or other videos. Because it is automated, it does not always have the correct word.
• Why would someone on the street ask such a question
• Either the problem was really bothering them, or it was a dare.
• Why do people keep walking up to me asking me these questions. Like, I don't know you, go away please.
• Answer the question or face judgement
• These people on the street really do like asking us math questions, don't they?
• What are the chances that someone would ask you a math question like this?
• I just found a really cool way to solve this!! Bc of the binomial therom, we know that the answer is going to be a binomial. We set our equation up like this: (x+2)(a+-b), and then work from there. x multiplied by what = x^2? x. So a = x. our equation is now (x+2)(x+-b), or when distributed, x^2+-bx+2x+-2b. Because the last term in our trinomial was ten, we know that b has too equal to 5, as 2*5 = 10. We can even check our work by putting in 5 for b in bx, and you get 5x+2x = 7x! Has this method been discovered before?
• Why did you assume that we multiply (x+2) with a polynomial of two terms (a+b)? why not (a+b+c) for example?
• if someone randomly came up to me on the street to ask a math equation I'd straight up run away
• That's what you should do
• Is factoring the expression faster/easier?
• Really it's whichever you prefer, and some may be easier one way for you and others would be easier the other.