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Answer
Simplify the expression \( \frac{x^{3}+4x^{2}-12}{x+3} \) to \( x^{2}+x-3-\frac{3}{x+3} \).
Solution
Calculate or simplify the expression \( (x^{3}+4x^{2}-12)/(x+3) \).
Divide the polynomials by following steps:
- step0: Using Long Division to Divide Polynomials:
\(\frac{\left(x^{3}+4x^{2}-12\right)}{\left(x+3\right)}\)
- step1: Calculate:
\(x^{2}+x-3+\frac{-3}{x+3}\)
La simplification de l'expression \( \frac{x^{3}+4x^{2}-12}{x+3} \) est \( x^{2}+x-3+\frac{-3}{x+3} \).
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Simplify this solution Extra Insights
Did you know that polynomial long division isn't just a math skill, but a powerful problem-solving tool? When you divide \( x^3 + 4x^2 - 12 \) by \( x + 3 \), you not only simplify the expression, but you also uncover insights into the function's behavior, such as its intercepts and asymptotes! As for common pitfalls, be wary of miscalculating your terms during long division. It’s easy to accidentally lose that sign or misalign your numbers! Always double-check your work at each step, especially when it comes to combining like terms and applying the remainder. A little care can save you from big headaches down the road!
