construct a polynomial third degree with zeros of -3, -1, and 2 and passes through (1,8)

Question

construct a polynomial third degree with zeros of -3, -1, and 2 and passes through (1,8)

Answer 1

f(x) = y = a(x+3)(x+1)(x-2)

8 = a(1+3)(1+1)(1-2)

8 = a(4)(2)(-1)

8 = a(-8)

a = 8/-8

a =-1

f(x) = -(x+3)(x+1)(x-2)

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

=-(x^3 +2x^2 -5x -6)

f(x) =-x^3 -2x^2 +5x +6 is the 3rd degree polynomial with the zeros -3,-1 & 2, going through (1,8)