Question

Find a polynomial f (x) of degree 4 that has the following zeros.

0, -8 (multiplicity 2), 7
Leave your answer in factored form.

Answer 1

`f(x)=x(x-7)(x+8)^2`

Explanation:

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

Therefore,

`x = 0`

`x = -8 \implies x + 8 = 0` (twice)

`x = 7 \implies x -7 = 0`

Write the polynomial as a product of its factors:

`f(x)=x(x-7)(x+8)^2`