Question

Find a polynomial f(x) of degree 3 that has the following zeros.1, -3, 0 Leave your answer in factored form.

Answer 1

Note that a polynomial in factored form :

$f(x)=(x-a)(x-b)(x-c)$

Has a, b and c as the zeros of the function.

From the problem, we have three zeros :

1, -3 and 0

Substitute these zeros to the function, we have :

$\begin{gathered} f(x)=\lbrack x-1\rbrack\lbrack x-(-3)\rbrack\lbrack x-0\rbrack \\ f(x)=(x-1)(x+3)(x)_{} \\ f(x)=x(x-1)(x+3) \end{gathered}$

The answer is

f(x) = x(x - 1)(x + 3)