What will the quotient and remainder be on division of $a x^{2} + b x + c$ by $p x^{3} + q x^{2} + r x + s, p \neq 0$ ?

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Solution

Since the degree of $p x^{3} + q x^{2} + r x + s$ i.e. $3$ is greater than $a x^{2} + b x + c$ i.e. $2$
So, the quotient on dividing $a x^{2} + b x + c$ by $p x^{3} + q x^{2} + r x + s$ will be $0$ and the remainder will be the dividend itself $a x^{2} + b x + c$

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Question1 (ii)
Answer the following and justify
What will the quotient and remainder be on division of $a x^{2} + b x + c$ by $p x^{3} + q x^{2} + r x + s, p \neq 0$ ?

Q. Question1 (ii)
Answer the following and justify
What will the quotient and remainder be on division of

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Q. On dividing a polynomial p(x) by a non-zero polynomial q(x), let g(x) be the quotient and r(x) be the remainder, than p(x) = q(x)⋅g(x) + r(x), where

(a) r(x) = 0 always
(b) deg r (x) <deg g(x) always
(c) either r(x) = 0 or deg r(x) <deg g(x)
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Q. If

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is a reciprocal equation of second type, then

Q. If

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, then the roots of

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

Since the degree of px3+qx2+rx+s i.e. 3 is greater than ax2+bx+c i.e. 2So, the quotient on dividing ax2+bx+c by px3+qx2+rx+s will be 0 and the remainder will be the dividend itself ax2+bx+c

What will the quotient and remainder be on division of $a x^{2} + b x + c$ by $p x^{3} + q x^{2} + r x + s, p \neq 0$ ?

Since the degree of $p x^{3} + q x^{2} + r x + s$ i.e. $3$ is greater than $a x^{2} + b x + c$ i.e. $2$
So, the quotient on dividing $a x^{2} + b x + c$ by $p x^{3} + q x^{2} + r x + s$ will be $0$ and the remainder will be the dividend itself $a x^{2} + b x + c$