We are asked for the remainder when dividing the cubic polynomial by a linear factor. First, identify the divisor: x + 1. Since the divisor is linear, the Remainder Theorem applies, which states that the remainder of f(x) divided by (x - a) is f(a). Here, x + 1 = x - (-1), so a = -1, and the remainder is f(-1). Compute f(-1) for f(x) = 2x^3 - 3x^2 + 4x + 5: - Evaluate 2(-1)^3 = 2(-1) = -2 - Evaluate -3(-1)^2 = -3(1) = -3 - Evaluate 4(-1) = -4 - The constant term is +5 Add them up: (-2) + (-3) + (-4) + 5 = -9 + 5 = -4. Therefore, the remainder is -4, which is an integer as requested. Note on the provided answer suggestion: if you were given 1/3 as the remainder, that would be inconsistent with the Remainder Theorem for this polynomial and divisor, so that option would be incorrect.

Questions

MCD2130 - T2 - 2025 6.8 Online Quiz MCD2130_QUIZ_FIVE Polynomials and Rational Functions

Short answer

MTH1010_05_05_1

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We are asked for the remainder when dividing the cubic polynomial by a linear factor. First, identify the divisor: x + 1. Since the divisor is linear, the Rem......Login to view full explanation

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