According to the Remainder Theorem, what is the remainder when P(x) = 2x^3 - 5x^2 + 4x - 7 is divided by (x - 2)?
Answer and explanation
Correct answer: C. -3
- Step 1: The Remainder Theorem states that dividing P(x) by (x - c) yields remainder R = P(c).
- Step 2: Here c = 2: P(2) = 2(2)^3 - 5(2)^2 + 4(2) - 7.
- Step 3: Evaluate powers: 2(8) - 5(4) + 8 - 7 = 16 - 20 + 8 - 7 = -4 + 8 - 7 = -3.
Answer
-3.
Why not the others: '5' miscalculates 16 - 20 as +4; '7' evaluates P(0); '-7' evaluates the constant term alone.
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