Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(10 g^{3}+22 g^{2}-24 g\right) \div(g+3) \) Submit

When dividing the polynomial \(10g^3 + 22g^2 - 24g\) by \(g + 3\), we can use polynomial long division. 1. Divide the leading term: \(10g^3 \div g = 10g^2\). 2. Multiply \(10g^2\) by \(g + 3\): \(10g^3 + 30g^2\). 3. Subtract: \((10g^3 + 22g^2 - 24g) - (10g^3 + 30g^2) = -8g^2 - 24g\). 4. Repeat with \(-8g^2\): \(-8g^2 \div g = -8g\). 5. Multiply: \(-8g(g + 3) = -8g^2 - 24g\). 6. Subtract again: \(-8g^2 - 24g - (-8g^2 - 24g) = 0\). Finally, since there's no remainder, the division is exact. Thus, the result is: \[ 10g^2 - 8g \]