When you factor a quadratic equation of the form #ax^2+bx+c#, you must find two numbers which, when multiplied, give #ac#, and when added, give #b#.

First let us compute #ac#.

#2*24=48#

Therefore, the two numbers add up to #19#, and multiply to give #48#.

List out the factors of #48#. I'm going to list them in pairs (each pair will multiply to give #48#, for example, #4# and #12#). You should be able to run through the factors in your head; listing out takes a lot of time.

#(1,48), (2,24), (3,16), (4, 12), (6,8)#.

Now, what of the above pairs add up to #19#? #3# and #16# do.

So now we have the equation, #2x^2+19x+24#

#=2x^2+16x+3x+24# (the factor pair)

#=2x(x+8)+3(x+8)#

#=(2x+3)(x+8)#

Factored.