\ac/
L V R
/ \
/ b \
where letters have their usual meaning. Comparing 8x² + 19x + 6 to ax² + bx + c,
ac = 8*6 = 48
b = 19
Factors of ac or 48 :-
1 * 48
2 * 24
3 * 16
As the sum of 3 and 16 is 19(or b), our required pair is 3 and 16.
On the left side:
L = 3/a = 3/8
On the right side:
R = 16/a = 16/8 = 2
Therefore, factorized form is (x + 3/8)(x + 2) which can be written as (8x + 3)(x + 2).
How this method works:
Make a X with ac and b on the top and bottom of the X, where ac and b are taken from ax² + bx + c.
On the left side we have d/a and e/a. Basically d and e are those values that we get after solving the whole question.
Step1: find the pair(s) for which sum of factors of ac = b. Here it is 3 and 16.
Step2: put these values in place of d and e.
Step3: solve left anf right of X,
Left = d/a = 3/8
Right = e/a = 16/8 = 2
Step4: whatever you get, put that in (x+?)(x+?) in place of ?.
