Question

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

 4x² − 5, 4x⁴ + 7x² + 15

Answer 1

\[(\frac{4 x^4 +^2 +15}{{4x}^2 -5}\]
\[ = \frac{x^2 {(4x}^2 {-5)+3(4x}^2 -5)+30}{{4x}^2 -5}\]
\[ = \frac{( {4x}^2 {-5)(x}^2 +3 ) +30}{{4x}^2 -5}\]
\[ {=(x}^2 +3 ) + \frac{30}{{4x}^2 -5}\]
\[ \because \text{Remainder = 30}\]
\[\text{Therefore,} (4 x^2 - 5) \text{is not a factor of}\ 4 x^4 + 7 x^2 + 15\]