Factor out the greatest common factor from each polynomial. See E...

Question

Factor out the greatest common factor from each polynomial. See Example 1. 4k^2m^3+8k^4m^3-12k^2m^4

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression. Six T. To the third. V. To the seventh minus 15 T. To the sixth. V. To the seventh plus 30 T. To the third V. To the ninth. And were asked to factor this expression, will we recall from previous lessons that we are going to look at each of these terms here that are being added or subtracted to one another. And then further than that we are going to look at the parts of each that are the same. So the whole numbers and compare those to each other. The tease, compare those to each other and the V. S. And compare those to each other. And for each of those three comparisons, we're going to ask ourselves, are there any factors that they share? Are there any things being multiplied in them that they share? That? We can factor out that we can pull out in front. So the first comparison here is with -15 and 30. Is there anything in each of those? Do they share? Any factors? Well, they're all divisible by three. So three is the greatest common factor that they share. So we can factor three out in front. How about with our T. S. We've got T to the third, T. To the sixth and T to the third. Well with our variables, we're going to look at the degrees and we're going to look for the lowest degree because that will be able to come out of all three of them? And the lowest degree here is three. So we're going to be able to take a. T. To the third out of all three of those teas. So we can factor a. T. To the third out in front. Alright. How about R. V. S. We have V. Two, the seventh V. To the seventh and V. To the ninth. And again we're going to look for the lowest degree out of 77 and nine. The lowest degree is seven. So we're able to take out of V. Two the seventh from each of those three V. Terms. So that's what we factored out in front. Now what's left now? We have to do that division that we set up on the right hand side. So for the first term we've got six divided by three. Well six divided by three is two. And then we also have T. To the third divided by T. To the third. Well that equals one. We don't have to put two times one there we can keep that as a two. And for the last part V. To the seventh divided by V. Two. The seventh again that is one. So we don't have to write that. Okay now let's work on the second one starting with negative 15 divided by three, negative 15 divided by three is negative five. T. To the sixth divided by T. To the third will recall that when we are dividing variables with exponents we are going to subtract those exponents from each other. So six minus three. So that will leave us with T. To the third left. And now V. To the seventh divided by V. Two. The seventh that is one. We do not have to put that times one in there. All right. Let's do the last one. I didn't underline that one. Alright. 30 divided by 3 30 divided by three is 10. So we have plus 10 then T. To the third, divided by T. To the third. That is one. We don't have to put that in there. And V. To the ninth divided by V. Two. The seventh while we take nine minus seven. So that leaves us with V squared. So 10 V. Squared. And we have done our factoring now we look at our answer choices and this matches with answer choice. C. Well done. We'll catch you on the next one.

Factor out the greatest common factor from each polynomial. See Example 1. 4k^2m^3+8k^4m^3-12k^2m^4

Key Concepts

Greatest Common Factor (GCF)

Factoring Polynomials

Polynomial Terms

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