College algebra question

Question

the polynomial of degree 3 p(x) has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x= -3. the y-intercept is y = -19.2.

find a formula for P(x)

Answer 1

If 4 is a root of multiplicity 2, then (x-4)² is a factor of the polynomial function.

If -3 is a root of multiplicity 1, then (x+3) is a factor.

That means we have:

P(x) = A (x-4)²(x+3).

Since the y-intercept is at (0, -19.2) that means when x = 0, y = -19.2:

-19.2=A(16)(3)

A = -19.2/48 = -2/5

So, P(x) = -2/5 (x-4)²(x+3)

If desired this can be expanded as shown here:

desmos.com/calculator/yuqlxdindf