Question

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

Answer 1

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

Explanation:

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