Can #y=x^3-4x^2+x-4+10 # be factored? If so what are the factors ?

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Answer 1 · 2017-01-17T14:04:04

#y=x^3-4x^2+x-4+10#

#y=x^3-4x^2+x+6#

Putting #x=-1# we get

#y=(-1)^3-4(-1)^2+(-1)+6#
#=-1-4-1+6=0#

So (#x+1#) is a factor of the polynomial of x

#y=x^3-4x^2+x+6#
#=x^3+x^2-5x^2-5x+6x+6#
#=x^2(x+1)-5x(x+1)+6(x+1)#

#=(x+1)(x^2-5x+6)#

#=(x+1)(x^2-3x-2x+6)#

#=(x+1){x(x-3)-2(x-3)}#

#=(x+1)(x-3)(x-2)#