Long Division of x^3-3x^2-10x+24 ÷x-2

see explanation

Step-by-step explanation:

  x - 2 |    x² - x - 12

          x³ - 3x² - 10x + 24

          x³  - 2x²    ↓       ↓      ← subtract terms from terms above

               - x²    - 10x + 24

               - x²   + 2x       ↓          ← subtract terms from terms above

                       - 12x + 24

                       - 12x + 24           ← subtract terms from above terms

                                    0 ← remainder

Since remainder is zero then (x - 2) is a factor

and quotient = x² - x - 12 , thus

x³ - 3x² - 10x + 24 = (x - 2)(x² - x - 12) = (x - 2)(x - 4)(x + 3)