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Let for a ≠ a1 ≠ 0, f(x) = ax² + bx + c, g(x) = a1x² + b1x + c1 and p(x) = f(x) − g(x). If p(x) = 0 only for x = −1 and p(−2) = 2, then the value of p(2) is:

1. 3
2. 9
3. 6
4. 18

Correct answer: 18

Solution

The polynomial p(x) is a quadratic function that has a double root at x = -1, meaning it can be expressed as p(x) = k(x + 1)² for some constant k. Given that p(-2) = 2, we can find k and subsequently calculate p(2), which results in p(2) = 18.

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