Rules of factoring, what about cross times?

Question

I need lots of helps please. learning an special techique but I need help.
Formula: acx^2+(ad+bc)x+bd=(ax+b)(cx+d)

In use. 2x^2+5x+3=(x+1)(2x+3)
ac (ad+bd) (bd)

To factor this type of polynomial the folowing cross-mutiplication method can be used to find the cofficents.

Can anybody tell me how I can use the cross-mutiplycation in finding the factor forms? Helps needed please

Answer 1

Factor 2 to give you possible combinations for a and c: (2, 1) is the only factoring, though we don't know which one is a and which one is c.
Similarly, we get 3 and 1 for b and d.
Write a and c in one column and b and d in another. (You can arbitrarily choose which order to take a and c in.) We cross-multiply to identify which ones need to be paired. There are two possibilities:
2 \ / 1
1 / \ 3
2×3 + 1×1 = 6 + 1 = 7

2 \ / 3
1 / \ 1
2×1 + 1×3 = 2 + 3 = 5

The second case gives you the correct result for ad + bc, so that represents the correct factorisation. So we have a = 2, b = 3, c = d = 1 for a factorisation of (2x+3)(x+1).