Question

find teh gcf and factor the expression. problem in comments. best answer and i will become a fan

Answer 1

\[4n^{2}-20n+24\]

Answer 2

The greatest common factor is the factor that is the largest present among all of your numbers. So:
4 has factors: 1, 2, 4
20 has factors: 1, 2, 4, 5, 10, 20
24 has factors: 1, 2, 3, 4, 6, 8, 12, 24

Which number is largest among all of them? 4 is! So you factor our the 4 from your expression. When you do you, you are essentially dividing out each term by 4 in the parentheses:

\[4n^2-20n+24=4(n^2-5n+6)\]

Answer 3

Now, in order to factor it out even more, there is a way to do this: You find two numbers (say you call them a and b) such that a*b=6 (the middle number), and a+b=-5 (the last number).
You can think of a=-2 and b=-3 (Why? because a*b = (-2)*(-3)=6 and a+b=(-2)+(-3)=-5)

So once you have these 2 numbers a,b, you write down your factors as: (n+a)(n+b). This will the general form to write out your factors. Then just substitute the values of a and b:
(n+(-2))(n+(-3)) = (n-2)(n-3)

Now you had a 4 initially before the parentheses: so you get 4(n-2)(n-3)

Answer 4

You can always double check your by multiplying out your factors:
4(n-2)(n-3) = 4[n^2-3n-2n+6] = 4[n^2-5n+6]=4n^2-20n+24