$The remainder when the polynomial p (x) = x^{100} - x^{97} + x^{3} is divided by (x + 1) is:$

5

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3

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1

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6

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Solution

The correct option is C $1$
$By remainder theorem, we know that if a polynomial f(x) is divided by (x - a), the remainder obtained is f(a).$

$Using remainder theorem, the remainder when p (x) is divided by (x + 1) is p (- 1) .$

$p (- 1) = (- 1)^{100} - (- 1)^{97} + (- 1)^{3} p (- 1) = 1 - (- 1) - 1 = 1$

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