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michelle95
find teh gcf and factor the expression. problem in comments. best answer and i will become a fan
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: \[4n^2-20n+24=4(n^2-5n+6)\]
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)
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