Answer:
[tex]3x^3-3x^2-6x[/tex]
Step-by-step explanation:
We have been given that the polynomial function has x intercepts –1, 0, and 2.
Thus, we have
[tex]f(x)=a(x+1)(x-0)(x-2)\\\\f(x)=ax(x+1)(x-2)[/tex]
Now, it passes through the point (1,-6). Hence, we have
[tex]-6=a(1)(1+1)(1-2)[/tex]
Solve the equation for a
[tex]-6=-2a\\\\a=3[/tex]
Therefore, the polynomial function is
[tex]f(x)=3x(x+1)(x-2)\\\\f(x)=(3x^2+3x)(x-2)\\\\f(x)=3x^3-6x^2+3x^2-6x\\\\f(x)=3x^3-3x^2-6x[/tex]
