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Remainder Theorem

Can x -3 be t...

Question

Can (x-3) be the remainder on the division of a polynomial polynomial p(x) by (2x+5)?justify your answer.

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Solution

(x+3) can not be the reminder on the division of a polynomial p(x) by 2x-5, because the degree of reminder should be less than the degree of divisor. In the given question, the degree of reminder is equal to the degree of divisor. Hence it is not possible.

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Q. Question 1 (i)
Answer the following and justify
Can

x^{2} - 1

be the quotient on division of

x 6 + 2 x^{3} + x - 1

by a polynomial in x of degree 5?

In the division of a cubic polynomial p(x) by a linear polynomial, the remainder is p(-2).So, the divisor must be

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