I'm completely lost.?

Question

Explain in your own words how to factor a polynomial of the form ax2 + bx + c when a is not equal to 1. Describe both the grouping approach as well as reversing FOIL. Contrast the two methods by means of an example. Discuss which is the best approach and why.

Answer 1

I do not use either. I use the "bottoms up" method. It works for any trinomial.
Here is a link that has an explanation of it.
http://mathforum.org/t2t/message.taco?thread=18119&message=1

I'll work an example

Let's say I want to factor this polynomial
2r^2 + 17r + 36 = 0

I'll go step by step to factor it, by the "bottoms up" method

Step 1 : Multiply Leading Coefficient by constant
2 * 36 = 72

Step 2 : Find two numbers that multiply to 72 and sum to 17
9 and 8

Step 3: Write the two previous factors as two multiplying factors
(r+9) (r+8)

Step4: Now divide both numbers by whatever your leading coefficient was, in our case it was 2

(r + 9/2) (r + 8/2)
==> (r+ 9/2) (r + 4)

After you divide , if one of the numbers is not a whole number (in our case 9/2 is not a whole number), take the denominator and put it in front of the variable like so
(r + 9/2) becomes (2r + 9)

So our factors are (2r+9) (r+4)