How to write Polynomial

Question

How do I write a polynomial that is of the lowest degree with zeroes of 4/3(multiplicity of 2) and -1/3(multiplicity of 1) and with f(0)= -32

Answer 1

Your polynomial should look like

C(3x - 4)²(3x+1) = 0 multiplicity of 2 means the root appears as a square. Note that fractions can be avoided by interpreting the zeros as the numerator * x and the denominator as a constant term. There has to be a sign change so that when you solve 3x-4 = 0, you get x = 4/3

Use f(0) =32 to solve for C. Plug in x = 0

C(-4)²(1) = 32 Therefore C = 2

I'll let you multiply it out if that is necessary.