[tex]\frac{p(x)}{x-3} = 4x-5 + \frac{6}{x-3} [/tex]
The polynomial p(x) can be found by multiplying 'x-3' to every term
[tex]p(x) = (4x-5)(x-3) + 6[/tex]
Now distribute and you have your answer.
[tex]p(x) = 4x^2 -12x-5x+15 +6 \\ \\ p(x) = 4x^2 -17x+21[/tex]
