The GCF is x.
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Notice that we can factor out 2x from both terms on the LH side: ... 4x2+6x=0. The greatest common factor of 4 and 6 is 2 . The greatest common factor of x2 and x ...
Well, isn't that just a happy little math problem we have here! To factor 2x-12, we can first look for the greatest common factor, which in this case is 2. So we can factor out the 2 to get 2(x - 6). And there you have it, a beautifully factored expression ready to bring joy to your mathematical world.
There is no greatest common multiple. Ever! If x were the greatest common multiple, then what about 2x? Since x is a multiple of 16 and 24 then so also is 2x, so that 2x is a COMMON multiple. And it would certainly be greater that x. So 2x is a common multiple that is greater than the greatest common multiple. What?!
First, pull out a GCF, or a greatest common factor, x, and continue from there. So it'll be x(x^3-3x+2). Then it would be x(x^2-2)(x-1) and there you have it.
There can be no greatest common denominator. Suppose x is the greatest common denominator. That requires that 39 divides x, 26 divides x and x is the greatest such number. But 39 will divide 2x and 26 will divide 2x and 2x is greater than x. So x could not have been a GCD.