Question

subtract. express your answer as a polynomial in standard form. (1 point)
(2x^3 + 7x^2 + 4x - 1) - (x^2 + 3x + 5) = \square

Explanation:

Step1: Distribute the negative sign

We have \((2x^{3}+7x^{2}+4x - 1)-(x^{2}+3x + 5)\). Distribute the negative sign to the second polynomial: \(2x^{3}+7x^{2}+4x - 1 - x^{2}-3x - 5\).

Step2: Combine like terms

• For \(x^{3}\) term: \(2x^{3}\) (no other \(x^{3}\) terms).
• For \(x^{2}\) terms: \(7x^{2}-x^{2}=6x^{2}\).
• For \(x\) terms: \(4x - 3x=x\).
• For constant terms: \(-1 - 5=-6\).

Putting it all together, we get \(2x^{3}+6x^{2}+x - 6\).

Answer:

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