# How do you factor by grouping x^3 – 4x^2 +x + 6?

May 17, 2015

Try x = -1 -> f(x) = -1 - 4 - 1 + 6 = 0, then one factor is (x + 1)
Next, divide algebraically or guess.

$f \left(x\right) = \left(x + 1\right) \left({x}^{2} - 5 x + 6\right)$.
The trinomial in parentheses can be factored to (x - 3)(x - 2).

Finally: f(x) = (x + 1)(x - 2)(x - 3).

Check by developing:
$\left(x - 2\right) \left(x - 3\right) = {x}^{2} - 3 x - 2 x + 6 = {x}^{2} - 5 x + 6$. OK

$f \left(x\right) = \left(x + 1\right) \left({x}^{2} - 5 x + 6\right) = {x}^{3} - 5 {x}^{2} + 6 x + {x}^{2} - 5 x + 6 =$
$= {x}^{3} - 4 {x}^{2} + x + 6$. OK