Find the quotient and the remainder (if any), when:

6x² + x - 15 is divided by 3x + 5.

(6x² + x - 15) ÷ (3x + 5)

Dividing 6x² + x - 15 by 3x + 5

$\begin{array}{l} \phantom{3x + 5)}{2x - 3} \ 3x + 5\overline{\smash{\big)}6x^2 + x - 15} \ \phantom{3x + 5}\underline{\underset{-}{}6x^2 \underset{-}{+}10x} \ \phantom{{3x + 5}6x^2 +}-9x - 15 \ \phantom{{3x + 5}6x^2 +}\underline{\underset{+}{-}9x \underset{+}{-} 15} \ \phantom{{3x + 5}6x^2 + 9x -} \times \end{array}$

Quotient = 2x - 3

Remainder = 0

Verification:

Quotient x Divisor + Remainder

= (2x - 3) $\times$ (3x + 5) + 0

= 2x $\times$ (3x + 5) - 3 $\times$ (3x + 5)

= 6x⁽¹⁺¹⁾ + 10x - 9x - 15

= 6x² + (10x - 9x) - 15

= 6x² + x - 15

= Dividend