2006-11-13T22:12:51Z https://www.matematicasies.com/polinomios-factorizar-489#comment32 2006-11-13T22:12:51Z

<p><span class="spip-puce ltr"><b>–</b></span> a) <img src='https://www.matematicasies.com/local/cache-TeX/bfa80fb25339d31def10c5281d2e7a7b.png' style="vertical-align:middle;" width="323" height="47" alt="x^3+3x^2-2x-6 = (x+3) \cdot (x^2-2)" title="x^3+3x^2-2x-6 = (x+3) \cdot (x^2-2)"> <br><span class="spip-puce ltr"><b>–</b></span> b) <img src='https://www.matematicasies.com/local/cache-TeX/6561f7190a55f5cba3148bc362f88813.png' style="vertical-align:middle;" width="537" height="47" alt="x^4+5x^3-7x^2-41x-30 = (x+1) \cdot (x+2) \cdot (x-3) \cdot (x+5)" title="x^4+5x^3-7x^2-41x-30 = (x+1) \cdot (x+2) \cdot (x-3) \cdot (x+5)"></p> <p><i>Notas</i>: Usando raíces reales, el polinomio a) se puede factorizar aún más:</p> <p>Si resolvemos la ecuación <img src='https://www.matematicasies.com/local/cache-TeX/fd482f95a42138f36a422a4d760a2090.png' style="vertical-align:middle;" width="93" height="47" alt="x^2-2=0" title="x^2-2=0"> obtenemos como soluciones <img src='https://www.matematicasies.com/local/cache-TeX/776d38019212c22011668a4da4268dbe.png' style="vertical-align:middle;" width="47" height="50" alt="\pm \sqrt{2}" title="\pm \sqrt{2}">, por tanto, la factorización completa sería:</p> <p><span class="spip-puce ltr"><b>–</b></span> a) <img src='https://www.matematicasies.com/local/cache-TeX/7705a0b2bb4f1597eb51c6ff881a32b4.png' style="vertical-align:middle;" width="423" height="50" alt="x^3+3x^2-2x-6 = (x+3) \cdot (x-\sqrt{2}) \cdot (x+\sqrt{2})" title="x^3+3x^2-2x-6 = (x+3) \cdot (x-\sqrt{2}) \cdot (x+\sqrt{2})"></p>