Question

Divide the first polynomial by the second in each of the following. Also, write the quotient and remainder:

5y³ − 6y² + 6y − 1, 5y − 1

Answer 1

\[\frac{5 y^3 - 6 y^2 + 6y - 1}{5y - 1}\]
\[ = \frac{y^2 (5y - 1) - y(5y - 1) + 1(5y - 1)}{(5y - 1)}\]
\[ = \frac{(5y - 1)( y^2 - y + 1)}{(5y - 1)}\]
\[ = ( y^2 - y + 1)\]
\[\text{Therefore,} \]
\[\text{Quotient = y^2 - y + 1 and remainder = 0}\]