Question

Write a polynomial function of least degree with integral coefficients that has the given zeros. -4, 1, 5

Answer 1

`\bf \begin{cases} x=-4\implies &x+4=0\\ x=1\implies &x-1=0\\ x=5\implies &x-5=0 \end{cases} \\\\\\ (x+4)(x-1)(x-5)=\stackrel{original~polynomial}{0} \\\\\\ (x^2+3x-4)(x-5)=y\implies x^3+3x^2-4x-5x^2-15x+20=y \\\\\\ x^3-2x^2-19x+20=y`