Match the polynomials with their respective remainder when divided by ( $x - 1$ ).

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Solution

According to the remainder theorem, the remainder obtained when a polynomial p( $x$ ) is divided by ( $x - a$ ) is p(a).

Hence,
The remainder obtained when $5 x + 8$ is divided by $(x - 1) = 5 \times 1 + 8 = 13$ ,
The remainder obtained when $x^{2} - 2 x + 1$ is divided by
$(x - 1) = 1^{2} - 2 \times 1 + 1 = 0$ ,
The remainder obtained when $x^{3} + x^{2} + 1$ is divided by
$(x - 1) = 1^{3} + 1^{2} + 1 = 3$ .

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Match the polynomials with their respective remainder when divided by (x−1).

Match the polynomials with their respective remainder when divided by ( $x - 1$ ).