Which is not a factor of x³ - 4x² + x + 6?

Question: Which is not a factor of x³ - 4x² + x + 6?

Solution:
Let,
f(x) = x³ - 4x² + x + 6
∴ f(2) = 2³ - 4 . 2² + 2 + 6
= 8 - 16 + 2 + 6
= 16 - 16
= 0
So, (x - 2) will be a factor.

Now,
x³ - 4x² + x + 6
= x³ - 2x² - 2x² + 4x - 3x + 6
= x²(x - 2) - 2x(x - 2) - 3(x - 2)
= (x - 2) (x² - 2x - 3)
= (x - 2) (x² - 3x + x - 3)
= (x - 2) (x + 1) (x - 3)