In Exercises 1–10, factor out the greatest common factor. x^2(2x+...

Question

In Exercises 1–10, factor out the greatest common factor. x^2(2x+5)+17(2x+5)

Accepted Answer

Hello. Today we're gonna be identifying the greatest common factor in a given expression. So the expression given to us is X times the quantity seven X plus three plus eight times the quantity seven X plus three. Now looking at the two terms given to us we have X times seven X plus three and eight times seven X plus three. But notice that both of them have the common factor of seven X plus three. That means that the greatest common factor to this expression is going to be seven X plus three and we're gonna go ahead and factor that out from this quantity. What it means to factor the greatest common factor is we're going through each term and dividing each term by our greatest common factor which is seven X plus three. And this is going to reduce down to one. This will reduce down to one. So the way that you write out the factored version now is you start by writing your greatest common factor which is seven X plus three and is being multiplied by the quantity left over after the division. So that's going to be X times one plus eight times one. Now X times one is just going to give us X and eight times one is just going to give us eight. So what this simplifies to is seven X plus three times X plus eight. And this is going to be the simplified version of our given expression. That also means that the solution to this problem is going to be be So I hope this video helps you in understanding how to factor out the greatest common factor, and I'll go ahead and see you all in the next video.

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