The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=2 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,108).

Question

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=2 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,108).

Answer 1

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

108 = (5-2)^2(5)(5+3) = 25(5)(8) = 1000?? to change 1000 to 108, multiply by 108/1000 = 0.108

f(x) = 0.108(x-2)^2(x)(x+3)