Question

Verify the division algorithm i.e. Dividend = Divisor × Quotient + Remainder, in each of the following. Also, write the quotient and remainder.

Dividend	Divisor
6y5 − 28y3 + 3y2 + 30y − 9	2y2 − 6

Answer 1

Quotient = \[3 y^3 - 5y + \frac{3}{2}\]

Remainder = 0
Divisor =  2y² -  6

Divisor x Quotient + Remainder =

\[(2 y^2 - 6) \left( 3 y^3 - 5y + \frac{3}{2} \right) + 0\]
\[ = 6 y^5 - 10 y^3 + 3 y^2 - 18 y^3 + 30y - 9\]
\[ = 6 y^5 - 28 y^3 + 3 y^2 + 30y - 9\]

= Dividend

Thus, Divisor x Quotient + Remainder = Dividend
Hence verified.