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4) \( 10 x^{2}-13 x+51 \) \( x^{4}-x^{3}-11 x^{2}-x-12 \) B) \( 2 x^{2}+3 \) \( x^{3}-2 x^{2}+x \) () \( \frac{x+4}{x^{3}-4 x^{2}+x+6} \)

Ask by Warner Powell. in Venezuela
Mar 15,2025

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Para ayudarte mejor, necesito saber qué tipo de problema deseas resolver con estas expresiones algebraicas. ¿Quieres simplificarlas, resolver ecuaciones, factorizar polinomios o encontrar raíces? Por favor, proporciona más detalles para que pueda asistirte de manera efectiva.

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Beyond the Answer

Did you know that polynomial expressions can be classified based on their degrees? For instance, the first polynomial you provided, \( 10x^2 - 13x + 51 \), is a quadratic, which means its highest exponent is 2. Quadratics can show a range of behaviors, including having no real roots, one real root, or two real roots, depending on the discriminant \(b^2 - 4ac\). When simplifying rational functions, like \( \frac{x + 4}{x^3 - 4x^2 + x + 6} \), it's essential to factor the denominator when possible. Common mistakes include overlooking potential roots or failing to simplify further. Always remember to check for any common factors in the numerator and denominator to make your life easier, and ensure you're dealing with the simplest form of the expression!

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