Answer:
12x ( 4x - 1 ) should be the answer you're looking for.
Explanation:
48x^2 -12x
First, both terms have x variables right? To find the greatest common factor, you need to find which variable is the smallest. The smallest variable is x, (not x^2!) so this is part of the GCF. Find the factors of 12 and 48. Next, find all the common factors and choose the largest one (in value). The GCF of 12 and 48 is 12, so the GCF of the expression 48x^2 - 12x is 12x. Now, you need to extract 12x from the equation.
1(48x^2 - 12x) [Multiply the parenthesis by one. Since you are extracting, divide the inside by the GCF and multiply the outside by the GCF.]
12x(48x^2/12x - 12x/12x) [This is what you get. Solve inside the parenthesis.]
12x(4x - 1) [This is the answer.]
Tip: When extracting and finding the GCF, make sure to divide by the GCF. Don't forget to put the GCF outside the parenthesis afterwards, or else the expression won't be the same from when you started! I only put 1 outside the parenthesis in hopes that you would understand better.
(Did it work? xP )
EXAMPLE: If I want 4x^2+2x to be factored out, I would choose 2 and x to be factored. This is the combination of the two GCF of the variables and values of the expression. I divide 4x^2+2x by 2x, and I get 2x+1. If I don't have parenthesis and the GCF outside of them, the answer 2x+1 is incorrect. It would have to be 2x(2x+1) [which is 2x*2x+1*2x which is 4x^2+2x, which was the original expression]. Hopefully this helped.