Question

find the remainder when polynomial X^3-2X^2+X+1 is divided by X+1​

Answer 1

Required Answer :

The remainder is - 3 when polynomial x³ - 2x² + x + 2 is divided by x + 1

Given :

• Polynomial —» x³ - 2x² + x + 1

• The polynomial is divided by x + 1

To find :

• The remainder

Solution :

⇒ x + 1 = 0

⇒ x = 0 - 1

⇒ x = - 1

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⇒ P(x) = x³ - 2x² + x + 1

Substitute the value of x in P(x) :

⇒ P(-1) = (-1)³ - 2(-1)² + (-1) + 1

⇒ - 1 - 2(1) - 1 + 1

⇒ - 1 - 2 - 1 + 1

⇒ - 4 + 1

⇒ - 3

Therefore, the remainder is - 3, when the polynomial x³ - 2x² + x + 1 is divided by x + 1 [By Remainder factor theorem.]