Question

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Fatore:
X²-X+6X-6

Answer 1

Resposta:

x²-x+6x-6=x²+5x-6=(x-1)(x+6)

Explicação passo-a-passo:

x²-x+6x-6=x²+5x-6

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}+5x-6=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=5~e~c=-6\\\\\Delta=(b)^{2}-4(a)(c)=(5)^{2}-4(1)(-6)=25-(-24)=49\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(5)-\sqrt{49}}{2(1)}=\frac{-5-7}{2}=\frac{-12}{2}=-6\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(5)+\sqrt{49}}{2(1)}=\frac{-5+7}{2}=\frac{2}{2}=1\\\\S=\{-6,~1\}$

x²+5x-6=(x-(1))(x-(-6))=(x-1)(x+6)