polinomios factorizar

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Factoriza los siguientes polinomios:

– a)
– b)

SOLUCIÓN

– a)

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

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

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

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

– b)

$\polyhornerscheme[x=3,resultstyle=\color{red},resultbottomrule,resultleftrule,resultrightrule]{x^3+x^2-33x+63}$

$\polyhornerscheme[x=3,resultstyle=\color{red},resultbottomrule,resultleftrule,resultrightrule]{x^2+4x-21}$

$\polyhornerscheme[x=-7,resultstyle=\color{red},resultbottomrule,resultleftrule,resultrightrule]{x+7}$

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