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

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