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

Answer 1

\[\text{Quotient} = 5 z^2 + \frac{10}{3}z + 11\]

\[\text{Remainder} = 54\]

\[\text{Divisor} = 3z - 6\]

\[\text{Divisor} \times \text{Quotient} + \text{Remainder} = (3z - 6)\left( 5 z^2 + \frac{10}{3}z + 11 \right) + 54\]

\[ = 15 z^3 + 10 z^2 + 33z - 30 z^2 - 20z - 66 + 54\]

\[ = 15 z^3 - 20 z^2 + 13z - 12\]

\[ = \text{Dividend}\]

\[Thus, \]

\[\text{Divisor} \times \text{Quotient} + \text{Remainder} = \text{Dividend}\]