4 is a zero of the cubic polynomial p(x) = x³ — 3x² — 6x + 8. Find the remaining zeros of p(x).

Given, 4 is a zero of polynomial p(x).

So (x – 4) is the factor of p(x).

Here, dividend polynomial = p(x) = x³ — 3x² — 6x + 8

and divisor polynomial = s(x) = x – 4.

Coefficients of x³, x², x and x° are 1, –3, –6 and 8 respectively.

Taking x – 4 = 0 we get x = 4

∴ p(x) = x³ — 3x² — 6x + 8

= (x – 4) (x² + x – 2)

= (x – 4) (x² – x + 2x – 2)

= (x – 4) (x(x – 1) + 2(x –1))

= (x – 4)(x + 2)(x – 1)

To find the remaining zeros, let p(x) = 0

i.e. (x – 4)(x + 2)(x – 1) = 0

∴ The remaining zeros of p(x) are –2 and 1.