If $p(x) = x^{3} - 3x^{2} + ax + 6$ has remainder $0$ when divided by $(x - 1)$, then $a$ equals

If $p(x) = x^{3} - 3x^{2} + ax + 6$ has remainder $0$ when divided by $(x - 1)$, then $a$ equals
  1. $-4$
  2. $4$
  3. $0$
  4. $-6$

Solution

$p(1) = 1 - 3 + a + 6 = 4 + a = 0 \Rightarrow a = -4$.

Asked in: MH-SSC-9

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