Just a heads up, this isn't a calculus problem.
Anyways, I believe you can only factor a quadratic strictly into the form when
You can still factor by grouping though.
In general for a quadratic equation ax^2 + bx + c = 0 for factorization just write the product of the coefficient of x^2 and constant, in this case ac. Thereafter find such factors of the product ac such that their sum is equal to the coefficient of x. there after split the middle term and group into factors.
The reason I put it in calculus is because im doing a partial fraction integral and need to seperate the denomenamtor.
I'm still confused how to use the quadratic formula to factor into (x )(x )
Because I get .5 and -1 from the quadratic formula
However graphing (x-.5)(x+1) does not give the same as the original equation :S
in this case your equation is 2x^2 + x - 1
step 1: Product of coefficient of x square 9 in this case = 2 0 and constant term 9 in this case = -1 ) is = -2
step 2. factors of -2 are
-2 = 1x -2 = -1 x 2
step 3. select the factors whose sum is equal to the coefficient of x. in this case 2 + ( -1 ) = 1
step 4. split the middle term with these factors.
2x^2 + 2x - x - 1 = 2x ( x + 1 ) -1 ( x + 1 ) = ( x+1 ) ( 2x - 1)