Question

When a certain polynomial is divide by binomial x-3, the result is 4x-5+6/x-3. What is the polynomial

Answer 1

$\frac{p(x)}{x-3} = 4x-5 + \frac{6}{x-3}$

The polynomial p(x) can be found by multiplying 'x-3' to every term
$p(x) = (4x-5)(x-3) + 6$

Now distribute and you have your answer.
$p(x) = 4x^2 -12x-5x+15 +6 \\ \\ p(x) = 4x^2 -17x+21$