Can x^2+7x+3 be factored using integers?

Question

I'm having trouble figuring out if x^2+7x+3 can be factored using integers because i've written out the p, q, p+q and pq, but i can't seem to come up with an answer that makes sense. Any guidance would be greatly appreciated, thanks!

Answer 1

You want to find integers p,q such that p+q=7 and p*q=3, if you plot q=7-p and q=3/p on the same graph and find out where the line and the curve intersect you will quickly find out there are no integer solutions.

 

 

Jim

Answer 2

x^2+7x+3 can't be factored into the product of two binomials of lower degree with integer coefficients

whenever a, b, and c, in this case 1, 7, and 3, are all odd numbers the trinomial is irreducible over the set of integers