Question

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

Answer 1

ii) Given that

$a{x}^2+bx+c$ is divided by $p{x}^3+q{x}^2+rx+s,p\ne 0$.
So, the dividend is $a{x}^2+bx+c$ and the divisor is $p{x}^3+q{x}^2+rx+s,p\ne 0$.
We see that the degree of the divisor > degree of the dividend.
Then,
quotient = 0 and remainder = $a{x}^2+bx+c$, which is the dividend.

Note:
If the degree of the dividend < the degree of the divisor, then the quotient will be zero and remainder is same as the dividend.