
02-15-2008
Ok I will try to help.
This is a trinomial:
x^2 + 8x - 20
It's called that since there's 3 terms. When you factor it you want to turn it into two binomials. (This is the reverse of the FOIL method- which you can use to check your answer.)
Here's how I learned it... let's take that sample trinomial.
x^2 + 8x - 20
So to factor it, multiply the coefficient of the first term by the coefficient of the last term : 1 times -20 = -20
Now you ask yourself, what two numbers add up to the coefficient of the 2nd term (8) and multiply to -20? The answer is 10 and - 2 as:
10 x - 2 = -20 and 10 + -2 = 8
So substitute x with those two terms:
x^2 - 2x + 10x - 20
So to factor it further group in twos:
(x^2 - 2x) + (10x - 20)
Take out the greatest common factors for each group:
x(x - 2) + 10(x - 2)
If those two inner ones match you've probably done it right.
So the answer is the two factors (keep the sign before the 2nd factor of course) times the inner or in math:
(x+10)(x-2)
Check it.
I believe you have to do something different if the first term's coefficient is not 1 but I'm not sure what or if you do... but that's how you do it if the first term's coefficient is one, for sure.
Edit: If you need the answer for x as well as the factor set each binomial equal to 0.
x + 10 = 0
So x = -10
x - 2 = 0
so x = 2
So the answers are 2 and -10, plug them in the trinomial to check if it outputs 0.
Last edited by Fsunka; 02-15-2008 at 05:52 PM.
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