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GATE 2016 CE (CE1) – Question 9

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

Which is a factor of $f(x)=2x^7+3x-5$?

  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 divides f(x) when f(a)=0. At a=1, f(1)=2+3−5=0. Therefore **x−1, B**, is a factor; this check avoids unnecessary polynomial division.