Question

Which polynomial function has x intercepts –1, 0, and 2 and passes through the point (1, –6)?

Answer 1

f(x) = 3x^3 - 3x^2 - 6x

Answer 2

`3x^3-3x^2-6x`

Explanation:

We have been given that the polynomial function has x intercepts –1, 0, and 2.

Thus, we have

`f(x)=a(x+1)(x-0)(x-2)\\\\f(x)=ax(x+1)(x-2)`

Now, it passes through the point (1,-6). Hence, we have

`-6=a(1)(1+1)(1-2)`

Solve the equation for a

`-6=-2a\\\\a=3`

Therefore, the polynomial function is

`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`