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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 + 4y4 + 4y3 + 7y2 + 27y + 6 | 2y3 + 1 |
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Solution
Quotient = 3y2 + 2y + 2
Remainder = 4y2 + 25y + 4
Divisor = 2y3 + 1
Divisor x Quotient + Remainder = (2y3 + 1) (3y2 + 2y + 2) + 4y2 + 25y + 4
= 6y5 + 4y4 + 4y3 + 3y2 + 2y + 2 + 4y2 + 25y + 4
= 6y5 + 4y4 + 4y3 + 7y2 + 27y + 6
= Dividend
Thus,
Divisor x Quotient + Remainder = Dividend
Hence verified.
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