Let p(x) be a polynomial. When p(x) is divided by (x - 1), it leaves 2 as the remainder. When p(x) is divided by (x – 2), it leaves 1 as the remainder. What is the remainder when p(x) is divided by (x – 1)(x – 2)?
- A. 3
- B. -3
- C. 3 - x ✓
- D. 3 - 2x
Correct Answer: C. 3 - x
Explanation
Let the remainder be ax + b. By the Remainder Theorem, P(1) = a(1) + b = 2 and P(2) = a(2) + b = 1. Solving these simultaneously gives a = -1 and b = 3. The remainder is -x + 3, or 3 - x.
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