Multiple choice

The term containing the highest power of x in the polynominal f(x) is $2x^4$. Two of the roots of the equation f(x) =0 are -1 and 2. Given that $x^2-3x+1$ is a quadratic factor of f(x), find the remainder when f(x) is divided by 2x-1

  1. 1$\displaystyle \frac{1}{8}$

  2. 2

  3. 0

  4. -1/3
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A Correct answer
Explanation

Given f(x) has roots -1, 2 and factor x^2-3x+1, f(x) = 2(x+1)(x-2)(x^2-3x+1). To find the remainder when divided by 2x-1, evaluate f(1/2). f(1/2) = 2(1.5)(-1.5)(0.25 - 1.5 + 1) = 2(1.5)(-1.5)(-0.25) = 1.125, which is 1 1/8.

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