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

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Answer 1 · 2015-11-22T01:17:41

First, you know that #x=1# is a root because ...

#1+1+1-3=0#

So, divide the function by #(x-1)# using synthetic or long division to get ...

#x^2+2x+3#

Now, this function has only imaginary roots, so use the quadratic formula ...

#x=[-2+-sqrt(2^2-4(1)(3))]/(2(1))=-1+-isqrt2#

In summary, here are the factors:

#(x-1)(x+1-isqrt2)(x+1+isqrt2)#

hope that helped