In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:
f(x) = x3-6x2+11x-6, g(x) = x2-3x+2
We have,
f(x) = x3-6x2+11x-6 and g(x) = x2-3x+2
In order to find g (x) = x2-3x+2 = (x – 1) (x – 2) is a factor of f (x) or not, it is sufficient to prove that (x – 1) and (x – 2) are factors of f (x)
i.e. We have to prove that f (1) = 0 and f (2) = 0
f (1) = (1)3 – 6 (1)2 + 11 (1) – 6
= 1 – 6 + 11 – 6
= 12 – 12
= 0
f (2) = (2)3 – 6 (2)2 + 11 (2) – 6
= 8 – 24 + 22 – 6
= 30 – 30
= 0
Since, (x – 1) and (x – 2) are factors of f (x).
Therefore, g (x) = (x – 1) (x – 2) are the factors of f (x).