Question

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

Answer 1

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

`f(x) = (x + 1)(x^2 - 5x + 6)`.
The trinomial in parentheses can be factored to (x - 3)(x - 2).

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

Check by developing:
`(x - 2)(x - 3) = x^2 - 3x - 2x + 6 = x^2 - 5x + 6`. OK

`f(x) = (x + 1)(x^2 - 5x + 6) = x^3 - 5x^2 + 6x + x^2 - 5x + 6 =`
`= x^3 - 4x^2 + x + 6`. OK