polinomios factorizar

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Factoriza los siguientes polinomios:

– a) x^3-6x^2+11x-6
– b) x^3+x^2-33x+63

SOLUCIÓN

– a) x^3-6x^2+11x-6

\polyhornerscheme[x=1,resultstyle=\color{red},resultbottomrule,resultleftrule,resultrightrule]{x^3-6x^2+11x-6}

\polyhornerscheme[x=2,resultstyle=\color{red},resultbottomrule,resultleftrule,resultrightrule]{x^2-5x+6}

\polyhornerscheme[x=3,resultstyle=\color{red},resultbottomrule,resultleftrule,resultrightrule]{x-3}

x^3-6x^2+11x-6 = \fbox{(x-1) \cdot (x-2) \cdot (x-3)}

– b) x^3+x^2-33x+63

$\polyhornerscheme[x=3,resultstyle=\colorred,resultbottomrule,resultleftrule,resultrightrule]x^3+x^2-33x+63$

$\polyhornerscheme[x=3,resultstyle=\colorred,resultbottomrule,resultleftrule,resultrightrule]x^2+4x-21$

$\polyhornerscheme[x=-7,resultstyle=\colorred,resultbottomrule,resultleftrule,resultrightrule]x+7$

$x^3-6x^2+11x-6 = \fbox(x-3)^2 \cdot (x+7)$