Question 1172699
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If it is factorable, then it is the product of two linear factors:<br>
{{{(ax+b)(cx+d) = (ac)x^2+(bc+ad)x+bd}}}<br>
where a, b, c, and d are integers.<br>
You want the product to be 3x^2+4x+1<br>
Equating coefficients, that means...
(1) ac=3
(2) bc+ad=4
(3) bd=1<br>
The only way for ac=3 to be a product of two integers is if a and c are 1 and 3.
The only way for bd=1 to be a product of two integers is if b and d are both 1.<br>
That make the only possible factorization<br>
{{{3x^2+4x+1 = (x+1)(3x+1)}}}<br>
That factorization give us the right coefficient for the middle term: bc+ad = 1(3)+1(1) = 3+1 = 4.<br>