that should of said

Zero: 5 - 3 i
for the one that stated use the given zero to find the remaining zeros of the function

h(x)=x^4-15x^3+60x^2+70x-816

To find the remaining zeros of the function h(x) = x^4 - 15x^3 + 60x^2 + 70x - 816, we can use the given zero which is 5 - 3i.

First, let's understand what it means for a number to be a zero of a function. A zero of a function is a value that, when substituted into the function, results in a value of zero.

Given that we have a complex zero, it means that the function has complex roots. Complex roots always occur in conjugate pairs. This means that if 5 - 3i is a zero, then its conjugate, 5 + 3i, will also be a zero. This is because complex conjugates have identical real parts and opposite imaginary parts.

Therefore, the additional zeros of the function h(x) are 5 + 3i and their conjugate 5 - 3i.

To find the remaining zeros, we can divide the given polynomial by the factors (x - (5 - 3i)) and (x - (5 + 3i)) using polynomial long division or synthetic division.

Since polynomial long division can be time-consuming to explain in text, let's use synthetic division in this case:

1. Set up the synthetic division table with the coefficients of the polynomial:
```
5 - 3i | 1 -15 60 70 -816
```

2. Start the synthetic division process by bringing down the first coefficient:
```
1
5 - 3i | 1 -15 60 70 -816
```

3. Multiply the divisor, 5 - 3i, by the current result, which is 1, and write the product beneath the -15:
```
1
5 - 3i | 1 -15 60 70 -816
-15 + 9i
```

4. Add the numbers in the second column:
```
1
5 - 3i | 1 -15 60 70 -816
-15 + 9i
_________________
1 -15 + 9i
```

5. Repeat steps 3 and 4 until all the coefficients have been processed:

```
1
5 - 3i | 1 -15 60 70 -816
-15 + 9i
_________________
1 -15 + 9i 45 - 27i
-15 + 9i 60 - 36i
__________________________________
1 -15 + 9i 45 - 27i 105 - 63i
```

6. The result of the synthetic division is the polynomial with one degree less than the original polynomial. In this case, the result is: x^3 - 15x^2 + 45x - 105.

Now, the zeros of the original function h(x) = x^4 - 15x^3 + 60x^2 + 70x - 816 are: 5 - 3i, 5 + 3i, and the zeros of the reduced polynomial x^3 - 15x^2 + 45x - 105 can be found using another method such as factoring, using the Rational Root Theorem, or using a graphing calculator.

By following these steps, you can find the remaining zeros of the given function h(x).