If $x^{3} - 3 x^{2} + 3 x - 7 = (x + 1) (a x^{2} + b x + c)$ , then find $a + b + c$ .

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Solution

Consider the given equation.
$x^{3} - 3 x^{2} + 3 x - 7 = (x + 1) (a x^{2} + b x + c)$ $. . . . . . . . . . . . . (1)$

Since, $(x + 1)$ is the factor, then we get
$x^{2} - 4 x + - 7 = a x^{2} + b x + c$

On comparing both sides, we get
$a = 1, b = - 4, c = - 7$

Therefore,
$a + b + c = 1 - 4 - 7 = - 10$

Hence, this is the answer.

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