Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \[ (-10 w+10) \div(5 w-3) \] Submit

To divide the polynomial \(-10w + 10\) by \(5w - 3\), follow these steps: 1. **Set Up the Division:** \[ \frac{-10w + 10}{5w - 3} \] 2. **Determine the Quotient:** Since both the dividend and the divisor are linear polynomials, the quotient will be a constant. Let \(a\) be this constant: \[ -10w + 10 = a(5w - 3) + R \] 3. **Solve for \(a\):** Compare the coefficients of \(w\) on both sides: \[ -10 = 5a \quad \Rightarrow \quad a = -2 \] 4. **Find the Remainder \(R\):** Substitute \(a = -2\) back into the equation: \[ -10w + 10 = -2(5w - 3) + R \\ -10w + 10 = -10w + 6 + R \\ 10 = 6 + R \quad \Rightarrow \quad R = 4 \] 5. **Write the Final Answer:** Combine the quotient and the remainder: \[ \frac{-10w + 10}{5w - 3} = -2 + \frac{4}{5w - 3} \] **Final Answer:** \[ -2 + \frac{4}{5w - 3} \]