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  • Answer the following and justify: If on division of a polynomial p (x) by a polynomial g (x), the quotients zero, what is the relation between the degrees of p (x) and g (x)?

Answer the following and justify: If on division of a polynomial p (x) by a polynomial g (x), the quotients zero, what is the relation between the degrees of p (x) and g (x)?

Answers (1)

Division algorithm theorem :- According to division algorithm if one polynomial p(x) is divided by the other polynomial g(x) is then the relation among p(x), g(x), quotient q(x) and remainder r(x) is given by

p(x) = g(x) × q(x) + r(x)

where degree of r(x) < degree of g(x)

i.e. Dividend = Division × Quotient + Remainder

In the given statement it is given that on division of a polynomial p(x) by a polynomial g(x), the quotient is zero.

The given condition is possible only when degree of divisor is greater than degree of dividend

i.e. degree of g(x) > degree of p(x).

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infoexpert21

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