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

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Solution

If we divide any polynomial by another polynomial, then the degree of divisor is always greater than the degree of remainder.

In the given question the degrees of remainder (x−2) and divisor (2x+3) are same

Therefore if we divide the polynomial P(x) by (2x+3), then (x−2) cannot be the remainder

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

If we divide any polynomial by another polynomial, then the degree of divisor is always greater than the degree of remainder. In the given question the degrees of remainder (x−2) and divisor (2x+3) are same Therefore if we divide the polynomial P(x) by (2x+3), then (x−2) cannot be the remainder