Question

Which linear expression is a factor of the polynomial function f(x) = x3 + 2x2 − x − 2?

Answer 1

The function
f(x) = x3 + 2x2 − x − 2
is a trinomial and it is expected that it has three factors corresponding to the three roots. The possible roots could 1, -1, 2, or -2. Trying out 1
f(1) = 1 + 2 - 1 - 2 = 0
According to the remainder theorem (x - 1) is a factor. By doing synthetic division
1 | 1 2 -1 -2
       1  3  2
     1  3 2  0
f(x) = (x - 1)(x2 + 3x + 2)
which can further be factored into
f(x) = (x -1)(x +1)(x + 2)
The three factors are
x-1
x+1
x+2
which are all linear expressions