To find a polynomial of degree 3 with the given zeros, we first represent each zero as (x - zero). Therefore, our zeros -5, 5, and 7 become (x - -5), (x - 5), and (x - 7), respectively. We can simplify (x - -5) to (x + 5).
Our polynomial can therefore be represented as a product of these terms. So, we have:
``
`
p(x) = (x + 5)(x - 5)(x - 7)
```
Next, we can simplify this expression using the distributive property step by step.
First, let's distribute the first two terms, (x + 5)(x - 5):
```
= x² - 25.
```
Next, multiply the simplified expression x² - 25 by (x - 7):
```
= x³ - 7x² - 25x + 175
```
So, the polynomial of degree 3 with the given zeros -5, 5, and 7 is p(x) = x³ - 7x² - 25x + 175.