Find a formula for P(X)

Question

The polynomial of degree 4, P(X), has a root of multiplicity 2 at X=3 and roots of multiplicity 1 at X=0 and X=-2. It goes through the point (5,98).

Answer 1

ax(x+2)(x-3)^2 through (5,98)

= ax(x+2)(x^2-6x+9)

= ax(x^3-4x^2-3x +18)

= a(x^4 -4x^3 -3x^2 +18x), plug in x=5, y=98 to solve for "a"

98=a(625 -500-75 +90) = 140a

a = 98/140 = 49/70 = 7/10

= (7/10)(x^4-4x^3-3x^2+18x) = P(x)

P(x) = 7x^4/10 - 4x^3/10 -3x^2/10 +56x/5