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
≠ 0 ? $

To do:

We have to find the quotient and remainder on division of \( a x^{2}+b x+c \) by \( p x^{3}+q x^{2}+r x+s, p

Solution:

Here,
Divisor $=px3 + qx2 + rx + s, p≠0$

Dividend $= ax^2 + bx + c$

We observe that,

Degree of divisor $>$ Degree of dividend

We know that,

If the degree of dividend is less than the degree of the divisor, then the quotient will be zero and the remainder is same as the dividend.

Therefore, by division algorithm,

Quotient $= 0$ and Remainder $= ax^2 + bx + c$