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

Step 1: Find quotient and remainder of the given expression.
When the degree of the divisor is greater than the degree of dividend. Then, the remainder will be dividends and the quotient will be equal to zero.
The degree of the divisor $p x^{3} + q x^{2} + r x + s$ is $3$ .
The degree of the dividends $a x^{2} + b x + c$ is $2$ .
Here, the degree of the divisor is greater than the degree of dividend.
Therefore, the remainder will be dividends $a x^{2} + b x + c$ and the quotient will be zero.
Hence, the remainder is $a x^{2} + b x + c$ and the quotient is zero.

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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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p x^{3} + q x^{2} + r x + s, p \neq 0

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is a reciprocal equation of second type, then

Q. If

- 3, 1, 8

are the roots of

p x^{3} + q x^{2} + r x + s = 0

, then the roots of

p (x - 3)^{3} + q (x - 3)^{2} + r (x - 3) + s = 0

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

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