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प्रश्न
Find whether the first polynomial is a factor of the second.
4x2 − 5, 4x4 + 7x2 + 15
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उत्तर
\[(\frac{4 x^4 +^2 +15}{{4x}^2 -5}\]
\[ = \frac{x^2 {(4x}^2 {-5)+3(4x}^2 -5)+30}{{4x}^2 -5}\]
\[ = \frac{( {4x}^2 {-5)(x}^2 +3 ) +30}{{4x}^2 -5}\]
\[ {=(x}^2 +3 ) + \frac{30}{{4x}^2 -5}\]
\[ \because \text{Remainder = 30}\]
\[\text{Therefore,} (4 x^2 - 5) \text{is not a factor of}\ 4 x^4 + 7 x^2 + 15\]
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