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When (x⁴ + 5x² + 7x - 8) is divided by (x - 1) the remainder is a, and when divided by (x + 2) the remainder is b. Find the value of (b - a).
- 5
- 9
- 14
- 19
Correct answer: 9
Solution
By the Remainder Theorem, a = f(1) = 1 + 5 + 7 - 8 = 5. And b = f(-2) = (-2)⁴ + 5(-2)² + 7(-2) - 8 = 16 + 20 - 14 - 8 = 14. Therefore b - a = 14 - 5 = 9.
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