Find the coefficient of $x^{2}$ in the product $(x + 1)(x + 2)(x + 3)$.

Find the coefficient of $x^{2}$ in the product $(x + 1)(x + 2)(x + 3)$.
  1. $3$
  2. $6$
  3. $11$
  4. $2$

Solution

$(x+1)(x+2) = x^{2} + 3x + 2$. $(x^{2}+3x+2)(x+3) = x^{3} + 3x^{2} + 3x^{2} + 9x + 2x + 6 = x^{3} + 6x^{2} + 11x + 6$. Coefficient of $x^{2}$ is $6$.

Asked in: IMO

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