In Exercises 65–92, factor completely, or state that the polynomi...

Question

In Exercises 65–92, factor completely, or state that the polynomial is prime. 2x^3−8a^2 x+24x^2+72x

Accepted Answer

Hello, today we're going to be factoring out the greatest common factor from the given expression. So what we're given is 12 x plus 30. Now, when we're trying to determine the greatest common factor, what we're really trying to figure out is what is the greatest common number that we can divide both of our quantities by and not have a remainder when we divide both of the quantities. Well, if we take a look at the coefficient 12 and the constant term the one thing that they both have in common is that they are multiples of six, C, six times two is going to give us 12 and six times five is going to give us 30. So that means that both 12 and 30 are divisible by six, which means that the greatest common factor between the two terms is going to be six. So what we're going to do is divide both of the terms by six. And if we divide each term by six, what we end up with is 12 X divided by six, which is going to give us two X and 30 divided by six, which is going to give us positive five. Now keep in mind that we've divided out a six from each term in this quantity. So what we've done is divide each term by six, then take out the greatest common factor afterward. So what we have after factory, not the greatest common factor Is a six in front of the quantity. So what we now have is six times two X plus five. And this is going to be the factored form of the given expression. And with that being said, the answer to this problem is going to be c so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 65–92, factor completely, or state that the polynomial is prime. 2x^3−8a^2 x+24x^2+72x

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