To subtract the polynomials, we first rewrite the expression clearly and make sure to distribute the negative sign correctly:
\[ (3x^4 - 8x^2 + 4x) - (9x - 5x^4 - 2x^2) \]
Now, distribute the negative sign to each term in the second polynomial:
\[ 3x^4 - 8x^2 + 4x - 9x + 5x^4 + 2x^2 \]
Next, combine like terms:
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For \(x^4\) terms: \(3x^4 + 5x^4 = 8x^4\)
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For \(x^2\) terms: \(-8x^2 + 2x^2 = -6x^2\)
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For \(x\) terms: \(4x - 9x = -5x\)
Now we can combine everything into one polynomial:
\[ 8x^4 - 6x^2 - 5x \]
Finally, writing it in standard form (terms in descending order of degree):
\[ 8x^4 - 6x^2 - 5x \]
This is the result in standard form.