2 x^2 – 4x + 3x – 6Now we’re going to group it by factoring out the greatest common factor of
the first two terms and the greatest common factor of the last two terms:
2 x (x – 2) + 3(x – 2)For the pièce de résistance (pee-ess-duh-ray-zis-tonse) we’re going to factor
out the common factor in both of these new terms, the (x – 2), giving us:
(2x + 3) (x – 2)Voilà, our factored form! To check our work, we can FOIL these two
binomials. You multiply the First terms of each binomial together, then multiply
the Outside terms, then the Inside terms, and finally the Last terms.
Sorry if this diagram hurts your brain. Just track the arrows as they go through the letters FOIL and it should make more sense.
—SamanthaYou can see for yourself that when we combine the like terms –4x and 3x, we
get 2x^2 – x – 6, which is, miracle of miracles, our original trinomial. So we did
indeed find the right binomials.
(2x + 3) (x – 2)Now to solve the whole equation, set each of these two binomial factors
equal to zero. Why? Because if the product of two factors is zero, then one of
those factors has to be zero. Don’t believe us? Go ahead, think of two non-zero
numbers that multiply to zero. It ain’t happening!
So we have:
(2x + 3) = 0 and (x – 2) = 0