Is #x+1# a factor of #x^2-x^2-(2+√2)x+√2?#

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Answer 1 · 2018-06-09T14:09:17

#color(blue)("No")#

#x^2-x^2-(2+sqrt(2))x+sqrt(2)#

This simplifies to:

#-(2+sqrt(2))x+sqrt(2)#

If #(x+1)# is a factor of this equation, then we know that:

#(x+1)=0=>x=-1#

Is a root of:

#-(2+sqrt(2))x+sqrt(2)=0#

Substituting #x=-1#

#-(2+sqrt(2))(-1)+sqrt(2)=0#

#2+2sqrt(2)!=0#

So #(x+1)# is not a factor: