Question

Write a polynomial function of least degree with intrrgral coefficents that jas given zeros

Answer 1

18)

In general, a polynomial function is given by the expression below

`f(x)=(x-c_1)(x-c_2)\ldots(x-c_n)\to\text{polynomial of degre}e\text{ equal to n}`

Therefore, in our case,

`g(x)=(x+1)(x-1)(x-4)`

Thus, the least degree of the polynomial is 3.

Expand g(x) as shown below

`\begin{gathered} \Rightarrow g(x)=(x^2-1^{})(x-4)\to(x-1)(x+1)=(x^2-1^2) \\ \Rightarrow g(x)=x^3-4x^2-x+4 \end{gathered}`

Hence, the answer is x^3-4x^2-x+4