Algebra 2 L.4 Divide polynomials using long division YN5 Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \[ \begin{array}{l}\left(-63 w^{3}-29 w^{2}+4 w\right) \div(7 w+4) \\ \text { Submit }\end{array} \]

To divide the polynomial \(-63w^3 - 29w^2 + 4w\) by \(7w + 4\) using long division, you would start by dividing the leading term of the dividend by the leading term of the divisor. 1. Divide \(-63w^3\) by \(7w\) to get \(-9w^2\). 2. Multiply \(-9w^2\) by \(7w + 4\) to get \(-63w^3 - 36w^2\). 3. Subtract this from the original polynomial: \[ (-63w^3 - 29w^2 + 4w) - (-63w^3 - 36w^2) = 7w^2 + 4w \] 4. Next, divide \(7w^2\) by \(7w\) to get \(w\). 5. Multiply \(w\) by \(7w + 4\) to get \(7w^2 + 4w\). 6. Subtract again: \[ (7w^2 + 4w) - (7w^2 + 4w) = 0 \] Since the result is zero, there is no remainder. Thus, the final answer is: \[ \frac{-63w^3 - 29w^2 + 4w}{7w + 4} = -9w^2 + w \] And if we were to have a remainder, remember to include it as a fraction over the divisor!