Question

Find a polynomial f(x) of degree 3 that has the following zeros.

Answer 1

Answer:

$f (x) = x (x + 5) (x-9)$

Step-by-step explanation:

The zeros of the polynomial are all the values of x for which the function $f (x) = 0$

In this case we know that the zeros are:

$x = 9,\ x-9 =0$

$x = 0$

$x = -5$, $x + 5 = 0$

Now we can write the polynomial as a product of its factors

$f (x) = x (x + 5) (x-9)$

Note that the polynomial is of degree 3 because the greatest exponent of the variable x that results from multiplying the factors of f (x) is 3