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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 |
| 15z3 − 20z2 + 13z − 12 | 3z − 6 |
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Solution
\[\text{Quotient} = 5 z^2 + \frac{10}{3}z + 11\]
\[\text{Remainder} = 54\]
\[\text{Divisor} = 3z - 6\]
\[\text{Divisor} \times \text{Quotient} + \text{Remainder} = (3z - 6)\left( 5 z^2 + \frac{10}{3}z + 11 \right) + 54\]
\[ = 15 z^3 + 10 z^2 + 33z - 30 z^2 - 20z - 66 + 54\]
\[ = 15 z^3 - 20 z^2 + 13z - 12\]
\[ = \text{Dividend}\]
\[Thus, \]
\[\text{Divisor} \times \text{Quotient} + \text{Remainder} = \text{Dividend}\]
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