Question

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

Answer 1

$\bf \begin{cases} x=-1\implies &x+1=0\\ x=0\implies &x=0 \end{cases} \\\\\\ \stackrel{\textit{multiplicity of 3}}{(x+1)^3}~~\stackrel{\textit{multiplicity of 1}}{(x)^1}=\stackrel{original~polynomial}{0} \\\\\\ (x^3+3x^2+3x+1)(x)=\stackrel{y}{0}\implies x^4+3x^3+3x^2+x=y$