Question

The cubic polynomial below has a double root at x=-4 and one root at x=6 and passes through the point (2,36) as shown. Algebraically determine it’s equation in factored form.

Answer 1

Answer: P(x) = (-1/4)*(x + 4)*(x + 4)*(x - 6)

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)