Find a polynomial function of degree 4 with -2 as a zero of multiplicity 3 and 0 as a zero of multiplicity 1

Answer 1

Since -2 is a zero, the factor would be (x+2), which we would cube to make a multiplicity of 3. Since 0 is also a zero, the factor would be x

f(x) = (x+2)³(x) = x⁴ + 6x³ + 12x² + 8x