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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 |
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Solution
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.
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