Question

Find whether the first polynomial is a factor of the second.

4y + 1, 8y² − 2y + 1

Answer 1

\[\frac{{8y}^2 -2y+1}{4y+1}\]
\[ = \frac{2y (4y+1)-1(4y+1)+2}{4y+1}\]
\[ = \frac{(4y+1)(2y-1)+2}{4y+1}\]
\[ = (2y-1)+ \frac{2}{4y+1}\]
\[ \because \text{Remainder = 2}\]
\[ \therefore \text{( 4y+1) is not a factor of}\ {8y}^2 -2y+1.\]