I have to construct a polynomial of least degree possible.

Question

Real roots: 4,2,14^,2,1 and contain the point (−3,−5)(-3,-5).

Answer 1

P(x) = a(x - 4)(x - 2)(x - 1); P(- 3) = a(- 3 - 4)(- 3 - 2)(- 3 - 1) = - 5; - 140a = - 5; a = 1/28

P(x) = 1/28(x - 4)(x - 2)(x - 1)