Factoring

(6) If you have this down well, the jump to non-monic quadratic trinomials is not bad . There are two
main strategies one can use here : (a) trial and error and (b) use group and hope . To get at either strategy, we
need a good handle on the ipop as in

The Left and Right products take care of themselves, the sign analysis as above still applies, but the ipop is our
main concern. All the coefficients and constants be low are positive :

(6a) In the trial and error method , we search for numbers A, B, a and b where AB = quadratic coefficient , ab =
constant and the ipop works out to be the linear term .
Some examples.

	trying the various factors of 6 and 2
	leads to
	trying the possibilities leads to
	keep trying:

(6b) In the use group and hope method we need to take a closer look at the (D), (E) and (F) forms above. The
linear coefficient in each case is the sum or difference of aB and Ab. Note that their product
[(aB)(Ab)=(AB)(ab)] is the product of the leading coefficient and the constant. Thus, if we form the product of
the leading coefficient and the constant, (AB)(ab), we try to find two numbers having this product and whose (a)
sum is the linear coefficient in forms (D) and (E) or whose (b) difference is the linear coefficient in form (F).
Some examples.

	so we need to find two
	numbers whose product is 12 and
	whose sum is 7. 3 and 4 do it.
	Group and hope
	Factor out 2x-1
	so we need to find two
	numbers whose product is 24 and
	whose sum is 14. 2 and 12 do it.
	Group and hope
	Factor out
	so we need to find two
	numbers whose product is 18 and
	whose DIFFERENCE is -7.
	works.
	Group and hope
	Factor out