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In $9-26,$ write each expression as the product of two binomials.$$3 x^{2}-5 x-12$$

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

Algebra

Chapter 1

THE INTEGERS

Section 6

Factoring Polynomials

The Integers

Equations and Inequalities

Polynomials

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Harvey Mudd College

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Lectures

01:32

In mathematics, the absolu…

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02:57

In $9-26,$ write each expr…

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So in this exercise we want to write This expression is a part of to buy no meals and we're gonna take it back to the beginning of the section. And remember how we used a trick to factor things like this but this one, if you're able to intuitively see how to factor it, great. But this was a bit of a trick. You're one to kind of just look at it and figure it out. So why don't we break this into four parts of three and then use that trick? Refined a factor between two terms and another two terms, And then we can write the product like that. So let's take this five x and break it down so we'll have three x squared instead of ready five x. Let's try something like How about we do? Instead of having a negative 12 we eat a term that we're going to be able to factor out. So if we do something like this kind of tricky to see, I would mitt but nine x plus four x o negative nine X plus four X. Now you might be thinking, How would you ever see something like that, but looking at three x squared, you're gonna be You will want to factor something with a three in it then. And of course, with five. There's not many ways to break that down. And to have a term that has three we could have done. Negative three x minus two X But then, if you kind of think ahead a little bit that to exterminate 12 wouldn't give you the same thing as a three expert. Enough. Three x. So even though it's really tricky to see here this negative Nynex and four X will give you that common factor of X minus three and again, as more practice as you don't want practice, it'll become easier to see. But really, the best thing I can say to you is that the three x squared to find something that factors with three. You're gonna need a three X and nine axes in the next 12 x. Very unlikely that that would've been the answer, but it's a possible thing that could have happened, but that is how he would kind of look at that. So let's take thes three x squared and negative Nynex term. And then let's take another pair of four accident. 12. So here, we're going to have taking a three. X out will have three x Times X minus three. Now what? This thing. We're going to have a four. That's comments will have plus four times X minus three. As you can see, that worked out and it was a hard one to see. But we have a X minus three. It's common between them so we can write her answer. All right, a little bit small here. Uh, nothing. Which room will have a X minus? Three term. Take the coefficients. We have three X plus four. But this was definitely a hard when I was just You look at it and kind of see, how would you recognize that? It will be a negative nine accident four X And of course, also if you kind of think of it like the ways of insane in previous videos, where you look at the constant with the sign of a law that might take a little bit longer, but it is also a way to approach it

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