^{2}+3b-18

^{2}-- that means that when you factor this expression, you'll get something that looks like (b+m)(b+n), where the

*m*and

*n*are constants of some kind. How do you find

*m*and

*n*, though?

^{2}+ bm + bn + mn, which can be rewritten with the Distributive Property as b

^{2}+ (m+n)b + mn.

^{2}+ 3b - 18: rewrite it as b

^{2}+ 3b

**+ -**18, so we can compare apples to apples, and match up the similar parts.

^{2}& b

^{2}: that's all good, we don't have to worry about that

**add up to 3**and

**multiply to -18**. From experience, I can tell you that since they multiply to a negative number, exactly one of those two numbers has to be negative. Since they add to a positive, though, the bigger number will be positive, and the smaller will be negative. (If you want more explanation on this conclusion, just ask!)

^{2}+3b-18?

^{3}or p

^{7}in there, or there's a k

^{2}but it's got a coefficient of 14 and is actually 14k

^{2}, this won't work). If your polynomial is x

^{2}+ bx + c, find two numbers that add to

*c*and multiply to

*b*, and then you can put them into your factors, (x+m) and (x+n). Easy!