Find quotient and remainder when $x^{2} + 5x + 7$ is divided by $x + 2$.

Find quotient and remainder when $x^{2} + 5x + 7$ is divided by $x + 2$.
  1. Quotient $x+3$, remainder $1$
  2. Quotient $x+3$, remainder $0$
  3. Quotient $x-3$, remainder $1$
  4. Quotient $x+5$, remainder $7$

Solution

Long division: $x^{2}+5x+7 = (x+2)(x+3) + 1$. So quotient $= x+3$, remainder $= 1$.

Asked in: IMO

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