 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2020/paper-1/1/solution

x^{2} + b x + c

. Comparing coefficients in

(x - 2) (x^{2} + b x + c)

with the given cubic polynomial gives

b - 2 = - 1

and

- 2 c = - 2

, hence

b = c = 1

x

is then

c - 2 b = - 1

, as required. Thus

x^{3} - x^{2} - x - 2 = (x - 2) (x^{2} + x + 1), other factor x^{2} + x + 1.

 New to topics? Read the docs here!