Divide:

6x³ - 13x² - 13x + 30 by 2x² - x - 6

Dividing 6x³ - 13x² - 13x + 30 by 2x² - x - 6

$\begin{array}{l} \phantom{2x^2 - x - 6)}{3x - 5} \ 2x^2 - x - 6\overline{\smash{\big)}6x^3 - 13x^2 - 13x + 30} \ \phantom{2x^2 - x - 6}\underline{\underset{-}{}6x^3 \underset{+}{-}\phantom{0}3x^2 \underset{+}{-}18x} \ \phantom{{2x^2 - x - 6}2x^3+}-10x^2 + 5x + 30 \ \phantom{{2x^2 - x - 6}2x^3+}\underline{\underset{+}{-}10x^2 \underset{-}{+} 5x \underset{-}{+} 30} \ \phantom{{2x^2 - x - 6}{2x^3+}{+5x^2222}}\times \end{array}$

Hence, (6x³ - 13x² - 13x + 30) ÷ (2x² - x - 6) = 3x - 5