Factorisation and factors

Question

Factorise $3x^2 + 26x + 51$. Hence , find the two factors of $32651$

Workings $$3x^2 + 26x + 51= (x+3)(3x+17) $$

I don't understand how can I use the answer above to help me find factors of $32651$

Answer 1

Let $x=100$,

Then $3x^2+26x+51=32651$

Hence $32651=(100+3)(3*100+17)$

It is easy to check both 317 and 103 are prime numbers.