Polynomials

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Polynomial Remainder Theorem

    What is the remainder when x4 + 5x3 – 3x2 + 4x + 3 is divided by x + 2?
    1. -41
    2. -31
    3. -18
    4. 41

 

  • Correct Answer
    Choice A. -41

Detailed Solution

When f(x) is divided by x-a , the reminder = f(a),
Here f(x) = x4 + 5x3 – 3x2 + 4x + 3
x + a = x + 2
a = -2
Therefore reminder = f(-2) = (-2)4 + 5(-2)3 – 3 (-2)2 + 4(-2) + 3
F(-2) = 16 - 40 - 12 - 8 + 3
F(-2) = -41
Hence remainder is -41


Correct Answer: -41.



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