The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = − 4 . The y -intercept is y = − 10.8 .

Question

formula?

Answer 1

x=-4

x+4=0

x+4 is one factor

x=3

x-3=0

x-3 is another factor

with multiplicity 2

x-3 is a 3rd factor

(x-3)(x-3)

= (x-3)^2

P(x)=a(x-3)^2(x+4)

P(0)=-10.8 =a(0-3)^2(0+4) = a(9)(4)

a = 10.8/36

a= 5.4/18 = 0.3

P(x) = .3(x-3)^2(x+4)

=.3(x^2-6x+9)(x+4)

=.3(x^3 -2x^2 -15x+36)

=3x^3/10 - 3x^2/5 - 9x/2 + 54/5

(no guarantee on the arithmetic, but that's the general method)