Factoring a Quadratic Trinomial by Grouping
Another method for factoring these kinds of quadratic trinomials is called factoring by grouping. Factoring by grouping can be a bit more tedious, and is often not worth the trouble if you can find the correct factors by some quick trial and error. However, it works quite well when the factors are not immediately obvious, such as when you have a very large number of candidate factors. When this happens, the trial and error method becomes very tedious
Factoring by grouping is best demonstrated with a few examples.
Given a general quadratic trinomial
ax2 + bx + c
1. Find the product ac.
2. Find two numbers h and k such that
hk = ac
(h and k are factors of the product of the coefficient of x2 and the constant term)
(h and k add to give the coefficient of x)
3. Rewrite the quadratic as
ax2 + hx + kx + c
4. Group the two pairs of terms that have common factors and simplify.
(ax2 + hx) + (kx + c)
x(ax + h) + (kx + c)
(note: because of the way you chose h and k, you will be able to factor a constant out of the second parentheses, leaving you with two identical expressions in parentheses as in the examples).
· Remember that this wont work for all quadratic trinomials, because not all quadratic trinomials can be factored into products of binomials with integer coefficients. If you have a non-factorable trinomial, you will not be able to do step 2 above.