Question
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
Ask by Boyd Gray. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The result of dividing \(10g^{3}+22g^{2}-24g\) by \(g+3\) is \(10g^{2}-8g\).
Solution
Calculate or simplify the expression \( (10g^3+22g^2-24g)/(g+3) \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{\left(10g^{3}+22g^{2}-24g\right)}{\left(g+3\right)}\)
- step1: Remove the parentheses:
\(\frac{10g^{3}+22g^{2}-24g}{g+3}\)
- step2: Factor the expression:
\(\frac{\left(g+3\right)\left(10g^{2}-8g\right)}{g+3}\)
- step3: Reduce the fraction:
\(10g^{2}-8g\)
The result of dividing the polynomial \(10g^{3}+22g^{2}-24g\) by \(g+3\) is \(10g^{2}-8g\).
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Simplify this solution Bonus Knowledge
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: \[ 10g^2 - 8g \]
