Verify the division algorithm i.e., Dividend = Divisor Quotient +… - Vidyadip

Question

Verify the division algorithm i.e., Dividend = Divisor $\times $ Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $6y^5- 28y^2+ 30y - 9$
Divisor: $2y^2- 6$

✓

Answer

Quotient $=3\text{y}^3-5\text{y}+\frac{3}{2}$
Remainder $=0$
Divisor $=2\text{y}^2-6$
Divisor $\times $ Quotient + Remainder = $\Big(2\text{y}^2-6\Big)\Big(3\text{y}^3-5\text{y}+\frac{3}{2}\Big)+0$
$=6\text{y}^5-10\text{y}^3+3\text{y}^2-18\text{y}^3+30\text{y}-9$
$=6\text{y}^5-28\text{y}^3+3\text{y}^2+30\text{y}-9$
$=\text{Dividend}$ Thus, Divisor $\times $ Quotient + Remainder = Dividend Hence verified.

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