How do you factor and find the zeroes for #F(x) = x^3 + x^2 + 4x + 4#?

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Answer 1 · 2015-06-06T10:51:13

Factor by grouping...

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

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

#= x^2(x+1)+4(x+1)#

#= (x^2+4)(x+1)#

The #(x^2+4)# factor has no linear factors with real coefficients since #x^2+4 >= 4 > 0# for all #x in RR#.

#F(x)=0# has one real root, viz #x = -1#