Question

Find the remainder when x3 – x² + x + 6 is divided by x + 1
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Answer 1

Answer :

Remainder = 3

Note :

★ Remainder theorem : If a polynomial p(x) is divided by (x - c) , then the remainder obtained is given as R = p(c) .

Solution :

Let the given polynomial be p(x) .

Thus ,

p(x) = x³ - x² + x + 6

If x + 1 = 0 , then x = -1 .

Thus ,

If p(x) is divided by x + 1 , then the remainder will be given as p(-1) .

Thus ,

=> R = p(-1)

=> R = (-1)³ - (-1)² + (-1) + 6

=> R = -1 - 1 - 1 + 6

=> R = 3

Hence ,

Remainder , R = 3