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In $27-39,$ factor each polynomial completely.$$4 a x^{2}+4 a x-24 a$$

$4a(x+3)(x-2)$

Algebra

Chapter 1

THE INTEGERS

Section 6

Factoring Polynomials

The Integers

Equations and Inequalities

Polynomials

Campbell University

Oregon State University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

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01:33

In $27-39,$ factor each po…

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Factor each polynomial com…

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So we want a factor, This expression completely. So just looking at all three times I see a common factor of or a or a Indiana 24 8 So we automatically know that we give back throughout A. And I also see some number coefficients that we can factor out. So the guy is coming back to between 44 and 24 would be four. So you came back two out of four eggs. And when we do that, well, it's with X squared plus X minus six on the inside. And you can check yourself by redistributing this back into are trying a meal and then we would end up with our original expression here. So now we want a factor. This China mule here. So we're gonna multiplier. First coat are coefficient times our last time, and we get negative six and we wanted to add to our little turn so there's gonna add Thio Positive one. So we need a list of factors of six which is one in sixth in two and three and because this six is negative and the positive times a negative gives us a negative, we know that only one of the turn One of the numbers and the pair can be negative. Bring for instance, if the one was positive, this six would have to be negative or the six was positive. The one would have to be negative. Only one number and the pair can be negative. So now we need to look at the combinations and figure out which combination will give us positively. So this is haven't the question. So now we're dealing with two in three and we know that Bream honest too, will give us positive one. So these two would be negative. It's never gonna split apart the middle term, this middle term here. So, you know, factored out for a and never going to have X squared. And they were gonna have minus two X plus three ex cause we split apart that term right there in minus six. So you gonna group this term and group this time together. So we still have four. I only outside. And now we're gonna back her out the greatest coming back to between one and negative to dust just one. And then the greatest common binomial between X squared existence fix. So we're less with X minus two on the inside and from our second pair were gonna factor out of three and look with X minus two on the inside. And we know we're on the right step. When this term matches this turn, So have for a Times X minus two times x plus three.

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