In Exercises 1–10, factor out the greatest common factor. 9x^4−18...

Question

In Exercises 1–10, factor out the greatest common factor. 9x^4−18x^3+27x^2

Accepted Answer

Hello, today we're going to be determining the greatest common factor from the given expression and using it to simplify the expression. So what we are given is five X to the fourth power minus 15 X to the third power plus X squared. Now, when we're trying to determine the greatest common factor, what we're really trying to ask ourselves is what is a common number that we can divide each term by without getting a remainder? Well, let's take a look at the, at the coefficients of each term first In the coefficients we have 5:15 and 45. And the one thing that these three numbers have in common is that they're all divisible by five. So we can go ahead and divide each term by five and that's going to be part of our greatest common factor. Now, one more thing to notice is that we have at least one instance of X squared in each of the terms. See the first term has X to the fourth, the second term has X to the third and the last term has X squared X to the fourth can be rewritten as X squared. Times X squared and X to the third can be rewritten as X squared times X. So we can go ahead and divide out an X squared from each of the terms. And that means that the greatest common factor for this expression is going to be five X squared. So let's go ahead and divide each of the terms by five X squared. In the first term, we have a five in the numerator and denominator and that's going to cancel it out. And X to the fourth divided by X squared is going to leave us with X squared in the numerator. In the second term, 15, divided by five is going to give us three and X cubed divided by X squared is just going to leave us with X. And in the last term, 45 divided by five is going to give us nine and X squared divided by X squared is just going to cancel itself out. So what we now have is X squared minus three X plus nine. But keep in mind that we factored out a five X squared from this quantity. So what we really have is five X squared times the quantity X squared minus three X plus nine. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a. 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 1–10, factor out the greatest common factor. 9x^4−18x^3+27x^2

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