What is the quotient when x^3-5x^2+5 is divided by x-2

x² - 3x - 6

Step-by-step explanation:

One way to divide is to use the divisor as a factor in the numerator

Consider the numerator

= x² (x - 2) + 2x² - 5x² + 5

= x² (x - 2) - 3x (x - 2) - 6x + 5

= x² (x - 2) - 3x (x - 2) - 6 (x - 2) - 12 + 5

= x² (x - 2) - 3x (x - 2) - 6 (x - 2) - 7

quotient = x² - 3x - 6, remainder = - 7