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Division of a Polynomial by a Monomial

A polynomial ...

Question

A polynomial
$P (x) = x^{2} + 2 x + 3$
leaves a remainder of ___ when divided by $x - 1$ .

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Solution

The correct option is D
6

From the remainder theorem,

The remainder when a polynomial P(x) is divided by (x – 1) is P(1).

$P (1) = 1^{2} + 2 (1) + 3 = 6$

Thus, the remainder = 6.

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