Question

Find a polynomial function of degree 5 with -3 as a zero of multiplicity​ 3, 0 as a zero of multiplicity 1​, and 3 as a zero of multiplicity 1.

Answer 1

$(x+3)^3\cdot x\cdot (x-3)=(x^3+9x^2+27x+27)\cdot (x^2-3x)=\\=x^5-3x^4+9x^4-27x^3+27x^3-81x^2+27x^2-81x=\\=x^5+6x^4-54x^2-81x$