MTH1010_05_05_1

Question

MTH1010_05_05_1

BlackTom AI · Accepted Answer

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.

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

MTH1010_05_05_1

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