Question

simplify.
$(6x^3 + x^5 + 2x^2 - 7 - 4x) - (3x^2 - 5x + 2 + 5x^5 + 3x^4)$
enter your answer, in standard form, in the box

Explanation:

Step1: Distribute the negative sign

First, we need to distribute the negative sign to the second polynomial. So, \((6x^{3}+x^{5}+2x^{2}-7 - 4x)-(3x^{2}-5x + 2+5x^{5}+3x^{4})\) becomes \(6x^{3}+x^{5}+2x^{2}-7 - 4x-3x^{2}+5x - 2-5x^{5}-3x^{4}\).

Step2: Combine like terms for \(x^{5}\)

Combine the terms with \(x^{5}\): \(x^{5}-5x^{5}=-4x^{5}\).

Step3: Combine like terms for \(x^{4}\)

The term with \(x^{4}\) is \(-3x^{4}\) (only one term, so it remains as is).

Step4: Combine like terms for \(x^{3}\)

The term with \(x^{3}\) is \(6x^{3}\) (only one term, so it remains as is).

Step5: Combine like terms for \(x^{2}\)

Combine the terms with \(x^{2}\): \(2x^{2}-3x^{2}=-x^{2}\).

Step6: Combine like terms for \(x\)

Combine the terms with \(x\): \(-4x + 5x=x\).

Step7: Combine constant terms

Combine the constant terms: \(-7-2=-9\).

Step8: Write in standard form

Now, write the polynomial in standard form (descending powers of \(x\)): \(-4x^{5}-3x^{4}+6x^{3}-x^{2}+x - 9\).

Answer:

\(-4x^{5}-3x^{4}+6x^{3}-x^{2}+x - 9\)