Factorize: x^4+x^3+x^2+2 ?

Question

# x^4+x^3+x^2+2#

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Answer 1 · 2018-05-08T15:24:37

#p(x)=(x^2-x+1)(x^2+2x+2)#

We know that,

#color(violet)((1)a^3+b^3=(a+b)(a^2-ab+b^2)#

We have,

#p(x)=x^4+x^3+x^2+2#

#color(white)(p(x))=x^4color(red)(-x^3)+x^2color(red)(+2x^3)+2#

#color(white)(p(x))=(x^4-x^3+x^2)+2(x^3+1)...tocolor(violet)((Apply(1))#

#color(white)(p(x))=x^2color(blue)((x^2-x+1))+2(x+1)color(blue) ((x^2-x+1))#

#color(white)(p(x))=(x^2-x+1)[x^2+2(x+1)]#

#color(white)(p(x))=(x^2-x+1)(x^2+2x+2)#