subtact the polynomail below and type in standard form.

(3x^4 - 8x^2 + 4x) - (9x - 5x^4 -2x^2)

1 answer

To subtract the polynomial \((9x - 5x^4 - 2x^2)\) from \((3x^4 - 8x^2 + 4x)\), we first rewrite the problem as follows:

\[ (3x^4 - 8x^2 + 4x) - (9x - 5x^4 - 2x^2) \]

Next, we distribute the negative sign through the second polynomial:

\[ 3x^4 - 8x^2 + 4x - 9x + 5x^4 + 2x^2 \]

Now, we can combine like terms:

  1. Combine \(x^4\) terms: \(3x^4 + 5x^4 = 8x^4\)
  2. Combine \(x^2\) terms: \(-8x^2 + 2x^2 = -6x^2\)
  3. Combine \(x\) terms: \(4x - 9x = -5x\)

Putting it all together, we have:

\[ 8x^4 - 6x^2 - 5x \]

This polynomial is now in standard form. Therefore, the final result is:

\[ \boxed{8x^4 - 6x^2 - 5x} \]