The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 4 and a root of multiplicity 1 at x = − 1 . The y -intercept is y = − 1.6 .

Answer 1

P(x) = a(x-4)^2(x+1)

= a(x^2 -8x +16)(x+1)

=a(x^3 -7x^2 +8x +16)

P(0) = 16a = 1.6

a= 1.6/16 = 0.1

P(x) = 0.1(x^3 -7x^2 +8x +16)

P(x) = x^3/10 -7x^2/10 +4x/5 +1.6