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GATE 2016 CS – Question 9

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

If $f(x) = 2x^7 + 3x - 5$, which of the following is a factor of $f(x)$?

  1. $(x^3 + 8)$
  2. $(x - 1)$
  3. $(2x - 5)$
  4. $(x + 1)$

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Show answer and explanation

Correct answer: (B) $(x - 1)$

Explanation

By the factor theorem, $(x - a)$ is a factor when $f(a) = 0$. Here $f(1) = 2 + 3 - 5 = 0$, so $(x - 1)$ is a factor. The other options do not give zero at their roots.