$If p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2 is divided by x - 1, then find the remainder.$

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Solution

By the remainder theorem, we know that if a polynomial f(x) is divided by (x - a), the remainder obtained is f(a).

$Given, polynomial, p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2 divided by (x-1).$

$The polynomial is divided by (x - 1) .$

$Then put (x - 1) = 0 \Rightarrow x = 1$

We get,

$P (1) = 2 (1)^{3} + 5 (1)^{2} - 3 (1) - 2$

$\Rightarrow p (1) = 2 + 5 - 3 - 2$

$\Rightarrow p (1) = 2 + 5 - 5$

$\Rightarrow p (1) = 2.$

$So, when p (x) = 2 x^{3} + 5 x^{2} - 3 x - 2 is divided by x - 1, the remainder obtained is 2.$

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