How do you solve (x2-2x-48) by (x-5) long division?

To divide ( x^2 - 2x - 48 ) by ( x - 5 ) using long division, first, determine how many times ( x ) goes into ( x^2 ), which is ( x ). Multiply ( x ) by ( x - 5 ) to get ( x^2 - 5x ) and subtract this from the original polynomial, resulting in ( 3x - 48 ). Next, determine how many times ( x ) goes into ( 3x ), which is ( 3 ). Multiply ( 3 ) by ( x - 5 ) to get ( 3x - 15 ) and subtract, resulting in ( -33 ). The final result is ( x + 3 ) with a remainder of ( -33 ), so the answer is ( x + 3 - \frac{33}{x-5} ).