Question

(x − 2) is a factor of x4 + 2x3 − 7x2 − 8x + 12. The other factors are

Answer 1

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

Explanation:

Factor the following:

x^4 + 2 x^3 - 7 x^2 - 8 x + 12

The possible rational roots of x^4 + 2 x^3 - 7 x^2 - 8 x + 12 are x = ± 1, x = ± 2, x = ± 3, x = ± 4, x = ± 6, x = ± 12. Of these, x = 1, x = 2, x = -2 and x = -3 are roots. This gives x - 1, x - 2, x + 2 and x + 3 as all factors:

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