Answer:
Option D is correct
The cubic polynomial function in standard form is :
[tex]x^3-x^2-4x+4[/tex]
Step-by-step explanation:
Given the zeroes of the polynomial function 1 , -2 and 2.
i.e, x = 1 , -2 and 2 where x is the zero of the polynomial function.
we can write this as
x - 1 = 0,
x + 2 = 0 or
x - 2 = 0
(x - 1)(x + 2)(x - 2) =0
Using identities [tex](a+b)(a-b) =a^2-b^2[/tex]
then;
[tex](x-1)(x^2-4)=0[/tex]
Multiply the first term of the first expression with second expression;
[tex]x (x^2-4) =x^3-4x[/tex]
also,
Multiply the second term of the first expression with second expression;
[tex]1(x^2-4) = x^2 -4[/tex]
Now, subtract [tex]x^3-4x[/tex] and [tex]x^2 -4[/tex]
we get;
[tex]x^3-4x-x^2+4[/tex]
then, we have;
[tex]x^3-x^2-4x+4=0[/tex]
Cubic function is any function of the form [tex]y = ax^3 + bx^2 + cx + d,[/tex] where a, b, c, and d are constants and a≠0
therefore, the given function is cubic function;
so, the cubic function f(x) = [tex]x^3-x^2-4x+4[/tex]
