Question

could i get a step by step explanation for factoring this trinomial?
i don't seem to understand how to get the final answer as i always get 2x(x+2)+x+2

2x^2+5x+2

Answer 1

It should be of form
(ax+b)(cx+d)
we need two numbers for bc and ad that add to 5, like 1 and 4
try
(2 x + 1)(x+2) = 2 x^2 + 1 x + 4 x + 2
which is
2 x^2 + 5 x + 2 whew !

Answer 2

by the way
2x(x+2)+x+2
is
2x(x+2 ) + 1(x+2)
which is
(2x+1)(x+2)
so you almost had it right

Answer 3

you do kind of a reverse FOILing

to get 2x^2 ... 2x and x

to get 2 ... 2 and 1

now pair them up to get 5x as the center term

(2x + 1) (x + 2) ... FOILing ... 2x^2 + 4x + x + 2