Find the quotient and the remainder when $2x^2 - 7x - 15$ is divided by $x - 2$.

(N/A) To find the quotient and remainder,we perform polynomial long division of $2x^2 - 7x - 15$ by $x - 2$.
Step $1$: Divide the first term of the dividend $(2x^2)$ by the first term of the divisor $(x)$ to get $2x$.
Step $2$: Multiply $2x$ by $(x - 2)$ to get $2x^2 - 4x$.
Step $3$: Subtract $(2x^2 - 4x)$ from $(2x^2 - 7x)$ to get $-3x$.
Step $4$: Bring down the next term $-15$ to get $-3x - 15$.
Step $5$: Divide the first term of the new expression $(-3x)$ by the first term of the divisor $(x)$ to get $-3$.
Step $6$: Multiply $-3$ by $(x - 2)$ to get $-3x + 6$.
Step $7$: Subtract $(-3x + 6)$ from $(-3x - 15)$ to get $-15 - 6 = -21$.
Thus,the Quotient $= 2x - 3$ and the Remainder $= -21$.