Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following cases: x³– 4x² + x + 6, g(x) = x – 3

(iii) p(x) = x³ – 4x² + x + 6 and g(x) = x – 3
Putting x – 3 = 0, we get, x = 3
Using remainder theorm, when p(x) = x³ – 4x² + x + 6 is divided by g(x) = x -3,
remainder is given by p(3)
= (3)³ – 4(3)² + (3) + 6
= 27 – 36 + 3 + 6 = 0
Since, remainder p(3) = 0, hence g(x) is a factor of p(x).