So it would be 3x2-5x+c / x+k and that would be = to 3x+1? If I solve that
No. The remainder is 3, and you can't ignore it.
Are you familiar with the "division algorithm", in which we expression division as
Dividend = Divisor * Quotient + Remainder ?
That's the form you want to write it in. You wrote it as an explicit division, but omitted the remainder.
Now, as has been suggested, you could alternatively carry out the division (3x
2-5x+c) / (x+k), using either long division or synthetic division; the coefficients you get will be expressions, not just numbers, so it might be confusing to you; that's what I don't recommend it. But it may be instructive.
In both methods, you need to use the fact that two polynomials are equal (that is, the same polynomial, not just the same number) when all coefficients are equal. So you'll be setting coefficients equal to one another.