How do you factor #x^3-4x^2-11x+30#?

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Answer 1 · 2018-04-16T09:12:07

#=>p(x)=(x-2)(x-5)(x+3)#

Here,

#p(x)=x^3-4x^2-11x+30#

For #x=2#,

#p(2)=2^3-4(2)^2-11(2)+30=8-16-22+30=0#

#=>(x-2)#, is a factor.

#:.p(x)=x^3-2x^2-2x^2+4x-15x+30#

#=>p(x)=x^2color(green)((x-2))-2xcolor(green)((x-2))-15color(green)((x-2))#

#=>p(x)=(x-2)(x^2color(red)(-2x)-15)#

#=>p(x)=(x-2)[x^2color(red)(-5x+3x)-15]#

#=>p(x)=(x-2)[xcolor(blue)((x-5))+3color(blue)((x-5))]#

#=>p(x)=(x-2)(x-5)(x+3)#