The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=0 and x=-4 , it goes through the point (5,72) Find a possible formula for P(x).

Answer 1

You use the zeros to find the factors.

f(x) = x(x-2)(x-2)(x+4) Now how do we account for that point?

72=a(5)(5-2)(5-2)(5+4) Add in an a for a possible stretch or shrink so the polynomial goes through that point

72=a(180) Divide by 180

a=2/5

f(x)=2/5x(x-2)(x-2)(x+4) You can multiply the factors out if needed.

Answer 2

P(x) = a(x - 0)(x - (-4))(x - 3)² = ax(x + 4)(x - 3)²

Since (5,72) is on the graph, 72 = 5a(9)(2)². Solve for a.