Polynomial functions — A/L Combined Mathematics

How do I practise Polynomial functions?

1 question with a worked solution

1. According to the Remainder Theorem, what is the remainder when the polynomial P(x) = 2x³ - 3x² + 4x - 5 is divided by (x - 2)?
   1. A) -3
   2. B) 9
   3. C) 5
   4. D) 7
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   Correct answer: D) 7

   By the Remainder Theorem, the remainder when a polynomial P(x) is divided by (x - a) is simply P(a). Here, a = 2. Evaluating: P(2) = 2(2)³ - 3(2)² + 4(2) - 5 = 2(8) - 3(4) + 8 - 5 = 16 - 12 + 8 - 5 = 7.

   Show worked solution

   Step 1: Apply remainder theorem: Remainder = P(2). Step 2: P(2) = 2(2)³ - 3(2)² + 4(2) - 5 = 16 - 12 + 8 - 5 = 7. Answer: 7.
   Modelled on: the A/L Combined Mathematics examination pattern

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Where does Polynomial functions fit in the syllabus?

Year 1 · Term 1