Can x-1 be the remainder on division of a pol | vedclass

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(B) No,$x-1$ cannot be the remainder.According to the Division Algorithm for polynomials,if a polynomial $p(x)$ is divided by a divisor $g(x)$,the rem

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No

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(B) No,$x-1$ cannot be the remainder.According to the Division Algorithm for polynomials,if a polynomial $p(x)$ is divided by a divisor $g(x)$,the remainder $r(x)$ must satisfy the condition that either $r(x) = 0$ or the degree of $r(x)$ is strictly less than the degree of $g(x)$.Here,the divisor is $g(x) = 2x+3$,which has a degree of $1$.The proposed remainder is $r(x) = x-1$,which also has a degree of $1$.Since the degree of the remainder is not less than the degree of the divisor,$x-1$ cannot be the remainder.

Can $x-1$ be the remainder on division of a polynomial $p(x)$ by $2x+3$? Justify your answer.

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