If one zero of the polynomial p(x) = x^{3} – 6x^{2} + 11x – 6 is 3, find the other two zeros.

It is given in the question that,

p (x) = x^{3} – 6x^{2} + 11x – 6 having factor (x + 3)

Now, we have to divide p (x) by (x – 3)

x^{3} – 6x^{2} + 11x – 6 = (x – 3) (x^{3} – 3x + 2)

= (x – 3) [(x^{2} – (2 + 1) x + 2]

= (x – 3) (x^{2} – 2x – x + 2)

= (x – 3) [x (x – 2) – 1 (x – 2)]

= (x – 3) (x - 1) (x – 2)

Hence, the two zeros of the polynomial are 1 and 2

17