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

Answer the following and justify: If on division of a non-zero polynomial p (x) by a polynomial g (x), the remainder is 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)          ….(1)

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

According to given statement on division of a non-zero polynomial p(x) by a polynomial g(x) then remainder r(x) is zero then equation (1) becomes

p(x) = g(x) × q(x)                    ….(2)

From equation (2) we can say g(x) is a factor of p(x) and degree of g(x) may be less than or equal to p(x).

 

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