Stop calling it LIOF. More with Reverse FOIL
Ax2 + Bx + C If A is 1, just looking for two numbers: They multiply to C They sum to B WATCH YOUR SIGNS Basics
It’s going to be easier (considering all the different things you have to remember this unit/quarter/year/life) to just PAY ATTENTION But for those of you with eidetic memories, here you go: If the third term (C) is +, both numbers have the same sign, which will match the sign on B If the C is -, B tells you the sign of the larger term. Note: This is not guaranteed if A is not 1. Signs
x2 + 13x + 22 x2 – 2x – 8 x2 – 7x + 6 x2 + 3x – 28 Examples
No shortcut. Deal with it. Find four numbers – two factors of A, two of C – that when some combination of products are added they give you B. The lower-case letter version of the quadratic form that I showed you last week hints at this. acx2 + (ad + bc)x + bd = (ax + b)(cx + d) What if A isn’t 1?
It’s guess and check, but obviously the better you are with the numbers (the more factors and multiples you know off the top of your head) the better off you’ll be. List the possible factors of A in one column, all the factors of C in another. Pair them off, look at possible multiples. Remember that (–) on C increases the number of multiples So what process do you follow?
3x2 + 13x + 10 6x2 + 11x – 35 Practice