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

Jun 6, 2015

Factor by grouping...

$F \left(x\right) = {x}^{3} + {x}^{2} + 4 x + 4$

$= \left({x}^{3} + {x}^{2}\right) + \left(4 x + 4\right)$

$= {x}^{2} \left(x + 1\right) + 4 \left(x + 1\right)$

$= \left({x}^{2} + 4\right) \left(x + 1\right)$

The $\left({x}^{2} + 4\right)$ factor has no linear factors with real coefficients since ${x}^{2} + 4 \ge 4 > 0$ for all $x \in \mathbb{R}$.

$F \left(x\right) = 0$ has one real root, viz $x = - 1$