Question

Consider the function f(x) = $\left\{ \begin{matrix} \frac{P(x)}{x - 2}; & x \neq 2 \\ 7; & x = 2 \end{matrix} \right.\$

where P(x) is a polynomial such that P′′′(x) is identically equal to 0 and P(3) = 9. If f(x) is continuous at x = 2, then P(x) is

• A. 2x² + x + 6
• B. 2x² – x – 6
• C. x² + 3
• D. x² – x + 7

Answer 1

Answer: (B)

2x² – x – 6

Answer 2

Let P(x) = ax² + bx + c,

then P(3) = 9, P(2) = 7 and $\lim _ { x \rightarrow 2 }$ $\frac{P(x)}{x - 2}$= 7