Question

subtact the polynomail below and type in standard form.

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

Answer 1

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:

- **For \(x^4\) terms:**
\(3x^4 + 5x^4 = 8x^4\)

- **For \(x^2\) terms:**
\(-8x^2 + 2x^2 = -6x^2\)

- **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.