Without actually dividing, find the remainder when x⁴ + x³ − 2x² + x + 1 is divided by x − 1, and justify your answer.

Question

TextRemainder Theorem for PolynomialsNCERT Exemplar

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If (x³ + ax² + bx + 6) has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), find the values of a and b.

If x⁵¹ + 51 is divided by x + 1, the remainder is

Remainder Theorem for Polynomials

Check whether p(x) is a multiple of g(x) or not, where p(x) = x³ – x + 1, g(x) = 2 – 3x

By Remainder Theorem find the remainder, when p(x) is divided by g(x), where

Check whether p(x) is a multiple of g(x) or not:

If the polynomials az³ + 4z² + 3z – 4 and z³ – 4z + a leave the same remainder when divided by z – 3, find the value of a.