factor f(x) = 3x^3 + 14x^2 - 23x + 6 into linear factors given that -6 is a zero of f(x)

Question

need help with this problem

Answer 1

f(x) = 3x^3 + 14x^2 - 23x + 6

If -6 is a zero of f(x), then we can write, x = -6, or equivalently, (x + 6) = 0.

This means (x + 6) is a factor of f(x), so we can take out that factor by dividing f(x) by (x + 6).

(x+6)(3x^2 - 4x + 1)   --- now factorise the quadratic

(x+6)(3x-1)(x-1)