Answer:
Step-by-step explanation:
Solving for x means you have to factor. First factor out the GCF of 2 to get:
[tex]2(3x^2+x-6)[/tex] and now we'll factor using the regular old method of ac and then factoring by grouping. In our polynomial, a = 3, b = 1, c = -6. Therefore, a times c is 3 * -6 which is -18. We need some combinations of the factors of 18 that will add to give us 1, the b term in the middle. The factors of 18 are:
1, 18
2, 9
3, 6 and that's it. Hm...it seems that won't work, so let's throw this into the quadratic formula, going back to the original and a = 6, b = 2 and c = -12:
[tex]x=\frac{-2+/-\sqrt{2^2-4(6)(-12)} }{2(6)}[/tex] and
[tex]x=\frac{-2+/-\sqrt{4+288} }{12}[/tex] and
[tex]x=\frac{-2+/-\sqrt{292} }{12}[/tex] and
[tex]x=\frac{-2+/-\sqrt{4*73} }{12}[/tex] and
[tex]x=\frac{-2+/-2\sqrt{73} }{12}[/tex] which finally simplifies to
[tex]x=\frac{-1+/-\sqrt{73} }{6}[/tex] No wonder that didn't factor using the traditional method of factoring! We could have found that out by finding first the value of the discriminant, but oh well!
