Use the given zero to find the remaining zeros of the function:

h(x)=x^4-15x^3+55x^2+155x-1476 Zero:5-4i

I multiplied [x-(5-4i)][x-(5+4i)] and got x^2-10x+9.

The example I have says to divide that by h and get a second quadratic equation that is also a factor of h. I have to use that equation to find the remaining zeros. How do I find the second equation?

(x-(5-4i))(x-(5+4i))

= (x-5+4i)(x-5 - 4i)
= x^2 - 5x - 4ix - 5x + 25 + 20i + 4ix -20i - 16i^2
= x^2 - 10x + 41

now divide x^4-15x^3+55x^2+155x-1476 by x^2 - 10x + 41 to get

x^2 - 5x - 36

(Google " long algebraic division" if you don't know how to do that)

now solving this quadratic:
x^2 - 5x - 36 = 0
(x-9)(x+4) = 0
x = 9, or x = -4

To find the second quadratic equation, you need to divide the polynomial h(x) by the quadratic equation you obtained, which is (x^2 - 10x + 9).

Perform polynomial long division by dividing h(x) by (x^2 - 10x + 9). The setup should look like this:

____________________________
x^2 - 10x + 9 | x^4 - 15x^3 + 55x^2 + 155x - 1476

Start by dividing x^4 by x^2, which gives you x^2. Then, multiply (x^2 - 10x + 9) by x^2, and subtract the result from h(x). The subtraction should eliminate the x^4 term.

Repeat this process for each term, bringing down the next term each time, until you reach a remainder of zero or the degree of the remainder becomes less than the degree of (x^2 - 10x + 9).

The result of the division will be another quadratic equation, which is the second factor of h(x). You can then solve this equation to find the remaining zeros of the function.

Keep in mind that dividing polynomials can sometimes be complex and time-consuming, so using a computer or a graphing calculator can be helpful in achieving an accurate result.