What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p≠0?


quotient = 0 and remainder = ax2 + bx + c

Let p(x) = ax2 + bx + c and g(x) = px3 + qx2 + rx + s , p≠0


Clearly the degree of divisor is greater than the degree of the dividend


i.e. deg (p(x)) < deg(g(x))


deg (p(x)) < deg (g(x)) × deg (q(x)) where deg (q(x)) can take any value …(1)


By division algorithm,


p(x) = g(x).q(x) + r(x)


Hence the degree in the L.H.S is equal to the degree of R.H.S


we know that the degree of r(x) will always be less than or equal to p(x)


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


(1) and (2) do not go hand in hand unless q(x) = 0


p(x) = g(x).q(x) + r(x)


= p(x) = 0 + r(x)


p(x) = r(x)


The quotient = 0 and the remainder is same as the dividend.


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