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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 |
| 4y3 + 8y + 8y2 + 7 | 2y2 − y + 1 |
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Solution
Quotient = 2y + 5
Remainder = 11y + 2
Divisor = 2y2 - y + 1
Divisor x Quotient + Remainder = (2y2 - y + 1) (2y + 5) + 11y + 2
= 4y3 +10y2 - 2y2 - 5y + 2y + 5 + 11y + 2
= 4y3 + 8y2 + 8y + 7
= Dividend
Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.
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