Answer: P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)
Step-by-step explanation:
The factored form of a polynomial is:
P(x) = A*(x - r₁)*(x - r₂)*(x - r₃)....
Where:
A is a real number.
r₁, r₂,.... etc
are the roots.
In this case, we know that the roots are:
-4, -4, and 6.
Then the polynomial will be:
p(x) = A*(x + 4)*(x + 4)*(x - 6)
Now we also know that this polynomial passes through the point (2, 36)
This means that:
P(2) = 36 = A*(2 + 4)*(2 + 4)*(2 - 6) = A*6*6*(-4) = A*(-144)
36 = A*(-144)
-36/144 = A
-0.25 = -1/4 = A
Then the polynomial is:
P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)
