Factor 2x²+13x+40

I thought with this sort of problem you are supposed to multipy 40 by 2 and get 80 and then come up with two factors that equal 13. If this doesn't work, you are supposed to factor out a number/variable.

Since neither of these methods work, is this problem unable to be factored, or am I mistaken?

Thanks in advance.

i thought it would be 15x3+40. I am not sure though

I don't think it can be factored. The factors of 40 are
40*1
20*2
10*4
8*5
and none of those number will work.

For

a x^2 + bx + c

calculate the discriminant:

b^2 - 4 a c.

If it is negative it cannot be factored.

In this case it is -151. The factorization involves the square root of the discriminant. If it isn't rational you won't be able to find the factorization by inspection easily either.