In Exercises 23–34, factor out the negative of the greatest commo...

Question

In Exercises 23–34, factor out the negative of the greatest common factor.

−4x + 12

Accepted Answer

Welcome back. I am so glad you're here. We are asked in the following expression, what is the negative, greatest common factor? And our expression is negative nine G plus 36. And our answer choices are A nine B negative nine C four and D negative four. Well, we recall from previous lessons on the greatest common factor. We're going to look at our terms here. We've got a negative nine G and a positive 36 we look at what's alike in them. Well, only the negative nine has a G attached to it 36 doesn't have a variable. So we're just going to be comparing the coefficient negative nine and the constant term positive 36. And we're going to say, what is the greatest common factor between those two numbers? The factors are the numbers that multiply to get us a number. So for negative nine, what can we multiply together to get negative nine? Well, we could take a negative one times a positive nine, we could also take a positive one times a negative nine. And the third option is we could take a negative three times a positive three. And now putting these in order, we would have the lowest one toward negative infinity would be a negative nine followed by a negative three, followed by a negative one, followed by a positive one and a positive three and a positive nine. Now let's figure out 36. What times what gives us 36? Well, that would be a one times 36 but it would also be a negative one times a negative 36. We can also have two times 18. We also have a negative two times a negative 18. We can take three times 13, no 12. Excuse me, that would also be a negative three times a negative 12. We can take a four times a nine. We'd also have a negative four times a negative nine and our last one would be six times six, but also negative six times negative six. And those are all of the factors. Putting those in order, let me switch colors here. Putting these in order would start from negative 36 to negative 18 to negative 12 to negative nine to a negative six. Then we'd have negative four, negative three, negative two and negative one and this would keep going. However, we are asked for the negative greatest common factor. So we have everything we need here. The most negative greatest common factor for negative nine, the one closest to negative infinity is negative nine is that shared by 36. Yes, it is. So the greatest common factor that's negative between the two of these is negative nine which matches with answer choice B well done. We'll catch you on the next one.

In Exercises 23–34, factor out the negative of the greatest common factor. −4x + 12

Key Concepts

Greatest Common Factor (GCF)

Factoring

Negative Factor

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