How is the "ac" method similar to the "undo FOIL" method?

Question

How is the "ac" method similar to the "undo FOIL" method? How is it different?

Answer 1

So when you work with trinomials, a lot of times you can find yourself guessing how to factor it. So let's say we have an expression like x²+6x+8, you could try and guess which numbers would give you a sum of 6 and product of 8.

But the faster way, ie, the AC method you mentioned, would be to label each part of the trinomial expression with the variables a, b, and c. Trinomials like this are written as ax²+bx+c, so in the aforementioned example, a=1, b=6, and c=8.

So by that logic, AC = 8 (because 1 x 8 = 8). So you need to find two numbers that give you a sum of b, which is 6, and ac, which is 8. In this case that's 2 and 4.

So then you break the expression into x²+2x+4x+8, and then group them as x(x+2)+4(x+2), which then gives you a factored expression of (x+2)(x+4).