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

Answer:

$3x^3-3x^2-6x$

Step-by-step 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

$f(x)=3x(x+1)(x-2)\\\\f(x)=(3x^2+3x)(x-2)\\\\f(x)=3x^3-6x^2+3x^2-6x\\\\f(x)=3x^3-3x^2-6x$