Question is:

4x^4 - 15x^2 + px + 6 / 2x+1 gives remainder 2/2x+1 .... Solve for p

My method in reviewing was to synthetically divide, and begin filling in what I could until p was surrounded, then I told it to put its hand up and surrender... It gave in, and I got the answer of 1.

But I did a test that had a slightly different question to it, but still a "solve for p" and I did it differently.. In that case, I was given a factor of the polynomial, and so I subbed it in to the equation (when that factor equalled zero) and set it all equal to zero... solved for p.

I just have a feeling there is a different way I could have done it here in the review...

Any ideas?