What factoring technique would be used to factor 2x^2+5x+3?

Answer 1

this is factoring of quadratic trinomials

because of the small numbers, it should be relatively easy to "guess" what the factors are
since the first term is 2x^2 the factors must start as
(2x + ?)(x + ?)
and since they end with a 3 the factors must end in 1 and 3
so it is either (2x+1)(x+3) or (2x+3(x+1)

it is easy to mentally check which gives us the 5x in the middle.

Answer 2

Trial and error. Whole number factors of 2 and 3 are limited, so it wont take long.

(2x+3)(x+1) Geepers, first try.

Answer 3

if you need a systematic way of factoring these, the method of "decomposition" seems to be a popular procedure taught these days.
Are you familiar with that?

Answer 4

Not really

Answer 5

I will illustrate with an example

6x^2 + 41x - 30

multiply the coefficients of the first and last terms.... 6(-30) = -180

now look for factors of -180 which add up to +41 ,(obviously one is + the other - )
after a few tries you should find -4 and +45
so now "decompose" the middle term of 41x into -4x + 45x

6x^2 + 41x - 30
= 6x^2 - 4x + 45x - 30
= 2x(3x-2) + 15(3x-2)
= (3x-2)(2x+15)

Answer 6

oh that's what you mean. I guess we call it something different. Thanks