1. ## Quadratic Delta Epsilon Proof

Please help me with this. I'm good with quadratic inequalities that I can factor, but I've never been able to wrap my head around ones that aren't factorable.

lim 0.1x^2+2.157x+20 = 203
x->33.33

2. If that limit is correct then the polynomial you will be working with is factorable!

If the limit as x goes to 33.33 of 0.1x^2+ 2.157x+ 20 is equal to 203, then 0.1x^2+ 2.157x+ 20- 203= 0.1x^2+ 2.157x- 183 would have to go to 0 and so must be factorable.

Using either "long division" or "synthetic division", divide 0.1x^2+ 2.157x- 183 by x- 33.33 to find the other factor.

(One difficulty is that the limit, as x goes to 33.33, is NOT exactly 203. I suspect you mean the limit as x goes to 100/3.)

3. Was this problem given with fractions or decimals? If it was given in fractions, please retype it, because I expect the fractions will be easier to work with.