# How do you factor x^3 -7x + 6 = 0?

Apr 1, 2016

(x - 1)(x - 2)(x + 3)

#### Explanation:

$f \left(x\right) = {x}^{3} - 7 x + 6$
Since (a + b + c + d = 0), then f(1) = 0 --> one factor if (x - 1).
After division -->
$f \left(x\right) = \left(x - 1\right) \left({x}^{2} + x - 6\right) .$
The trinomial in parentheses can be factored.
Find 2 numbers knowing sum (1) and product (-6). They are -2 and 3.
Therefor,
$f \left(x\right) = \left(x - 1\right) \left(x - 2\right) \left(x + 3\right)$