Question 760604
You are looking for two numbers, h and k, so that hk=3 and h+k=4.  You need for h and k to be rational numbers or preferably integers.  Based on the signs in the given polynomial, both h and k must be positive.  Your only choice (for integers) is 3 and 1 which will work.


Another structuring of the search:
{{{(x+h)(x+k)}}}=?
{{{x^2+hx+kx+hk}}}
{{{x^2+(h+k)x+hk}}}
How can {{{x^2+(h+k)x+hk=x^2+4x+3}}} ?



{{{x^2+4x+3}}} is factorable.
If let h=3, and k=1, then you have
{{{highlight((x+1)(x+3))}}}
Because 3*1=3 and 1+3=4