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Consider the polynomials $p(x)=(5x^2+6x+1)(x+1)(2x+3)$ and $q(x)=(5x^2-9x-2)(2x^2+5x+3)$. The set of common divisors of $p(x)$ and $q(x)$ is:

  1. $\{2x+3,\;x+1,\;5x+1\}$
  2. $\{2x+3,\;x-1,\;5x+1\}$
  3. $\{x+3,\;2x+1,\;x-2\}$
  4. $\{2x-3,\;x+1,\;5x+1\}$
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$p(x) =(5x^2+6x+1)(x+1)(2x+3)=(5x+1)(x+1)^2(2x+3) $

And

$q(x) =(5x^2-9x-2)(2x^2+5x+3) \\= (5x^2-10x+x-2)(2x^2+2x+3x+3)= (5x+1)(x-2)(2x+3)(x+1) $

$\therefore$ Common divisors are A.$\{ 2x+3, x+1, 5x+1\}$

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