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## More with Reverse FOIL

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**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