SOLUTION: Hi. How do you solve x^2 + 12x +8 ? We had to rationalize it (put it into the FOIL form. I.e: (x+4)(x+2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi. How do you solve x^2 + 12x +8 ? We had to rationalize it (put it into the FOIL form. I.e: (x+4)(x+2)      Log On


   

Question 875730: Hi. How do you solve x^2 + 12x +8 ? We had to rationalize it (put it into the FOIL form. I.e: (x+4)(x+2)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial does not need any rationalizing. The expression is already rational, if this applies at all. If you want to factorize the quadratic polynomial, you can try by logical guess and test; or you can check the discriminant.

The constant 8 can be 8*1 or 2*4; neither will give your coefficient of 12 for the 12x term.

Discriminant is 12%5E2-4%2A1%2A8=144-32=112, not a square.

What do you really want to be able to do? Find the roots? Factorize? Convert to standard form?

If you want to find the "roots", or "zeros", then you are interested in solving x%5E2%2B12x%2B8=0.
Directly using general solution for a quadratic formula,
x=%28-12%2B-+sqrt%28discriminant%29%29%2F%282%2A1%29
x=%28-12%2B-+sqrt%28112%29%29%2F2
x=%28-12%2B-+sqrt%2814%2A8%29%29%2F2
x=%28-12%2B-+sqrt%282%5E4%2A7%29%29%2F2
x=%28-12%2B-+4sqrt%287%29%29%2F2
highlight%28x=-6%2B-+2sqrt%287%29%29