Question

Identify the GCF
6x^2 and -54x^2

Answer 1

\[6x ^{2}\]

Answer 2

\[-54x ^{2}\]

Answer 3

Yeah, I just need helkp on identifying the gcf's of them aha.

Answer 4

i Really need the help man

Answer 5

I'll do a different problem as a demonstration of how to do it

Write all the quantities in their factored form
\[12x^2 = 2^2*3*x^2\]\[18x^3y = 2*3^2*x^3*y\]

Now to construct the GCF, you multiply together the largest common factors you've found:
\[GCF(12x^2,18x^3y)=2*3*x^2 = 6x^2\]

We took 1 \(2\) because that was the highest power of \(2\) that appeared in both. We took 1 \(3\) for the same reason. We took \(x^2\) because that was the highest power of \(x\) that appeared in both, and we left \(y\) whimpering in the corner, because it did not appear in both expressions.

If you divide both quantities by our GCF, you can see that this is the best we can do:
\[\frac{12x^2}{6x^2} = 2\]\[\frac{18x^3y}{6x^2} = 3xy\]
No more common factors remain in the quotients, so we can't stuff anything more into the GCF. Does that make sense?