Question

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=−2. Its lead coefficient is 2.

Answer 1

if

x = 3 is a root then (x -3) is a factor

multiplicity tells you how many times the root occurs

so you have 2 roots at x = 3 so 2 factors (x-3)(x-3)

so looking at the other roots

x = -2 then (x + 2) is a factor

x = 0 then x is factor

so

P(x) = a[x(x + 2)(x-3)(x-3)]

so to have the coefficient of x^4 as 2 then a = 2

hope it helps... just multiply it out

Answer 2

thank you!