If P(x) = x^4 - 2x^3 + 3x^2 - 4x + 2, what is the value of P(1) and what does it indicate about (x - 1)?
Answer and explanation
Correct answer: D. P(1) = 0
- Step 1: Substitute x = 1 into P(x): P(1) = 1^4 - 2(1)^3 + 3(1)^2 - 4(1) + 2 = 1 - 2 + 3 - 4 + 2 = 0. Step 2. By the factor theorem, P(1) = 0 proves that (x - 1) is a factor of P(x). Answer: P(1) = 0. Why not the others: The factor theorem states P(c) = 0 if and only if (x - c) divides P(x).
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