F.4 maths --simplify

Let f(x)=x^3- 2x^2 - 2x - 3
f(3)=3^3-2(3)^2-2(3)-3=0
∴(x-3)is a factor of f(x).
Use long division
f(x)=(x-3)(x^2+x+1)
∴ x^3- 2x^2 - 2x - 3
=(x-3)(x^2+x+1)

x^3 - 2x^2 - 2x - 3
=(x-3)(x^2+x+1)

Let f(x) = x^3 - 2x^2 - 2x - 3

f(3) = 27 - 18 - 6 - 3 = 0

(x - 3) is a factor

So, f(x) = (x - 3)(x^2 + x + 1)