Question

$ The polynomial 3x3 + 10x2 - x - 12 has a factor of x + 3. Find the remaining factors,

Answer 1

(3 x + 4) (x - 1) (x + 3)

Explanation:

Factor the following:

3 x^3 + 10 x^2 - x - 12

The possible rational roots of 3 x^3 + 10 x^2 - x - 12 are x = ± 1/3, x = ± 2/3, x = ± 4/3, x = ± 1, x = ± 2, x = ± 3, x = ± 4, x = ± 6, x = ± 12. Of these, x = -4/3, x = 1 and x = -3 are roots. This gives 3 x + 4, x - 1 and x + 3 as all factors:

Answer: (3 x + 4) (x - 1) (x + 3)