Question

Write a polynomial function of least degree with the given zeros: -2, 1,4

Answer 1

Since we want a polynomial p(x) with zeros -2,1 and 4, we have the following expression:

`p(x)=(x-(-2))(x-1)(x-4)`

If we multiply these factors we get:

`\begin{gathered} p(x)=(x+2)(x-1)(x-4) \\ \Rightarrow p(x)=(x^2+x-2)(x-4) \\ \Rightarrow p(x)=x^3-4x^2+x^2-4x-2x+8 \\ p(x)=x^3-3x^2-6x+8 \end{gathered}`

Therefore, the polynomial function with the given zeros is p(x)=x^3-3x^2-6x+8