Question

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

2a − 3, 10a² − 9a − 5

Answer 1

\[\frac{{10a}^2 -9a-5}{2a-3}\]
\[ = \frac{5a(2a-3)+3(2a-3)+4}{2a-3}\]
\[ = \frac{(2a-3)(5a+3)+4}{2a-3}\]
\[ =(5a+3)+ \frac{4}{2a-3}\]
\[ \because \text{Remainder = 4}\]
\[ \therefore \text{( 2a-3) is not a factor of}\ {10a}^2 -9a-5.\]