given that one of the zeros of the funiction f(x)=x^3-8x^2+11x+20 is -1, find the sum of the other zeros.

hwo do i do this?

To find the sum of the other zeros of the function, we need to use the fact that in a cubic polynomial, the sum of all the zeros is equal to the opposite of the coefficient of the quadratic term divided by the coefficient of the cubic term.

In this case, the given function is f(x) = x^3 - 8x^2 + 11x + 20. We are given that one of the zeros is -1.

To find the sum of the other zeros, we first need to find the quadratic polynomial that results when we divide f(x) by (x + 1).

Performing long division or synthetic division, we divide f(x) = x^3 - 8x^2 + 11x + 20 by (x + 1):

x^2 - 9x - 20
------------------
x + 1 | x^3 - 8x^2 + 11x + 20
- x^3 + x^2
---------------
-9x^2 + 11x
+ 9x^2 - 9x
------------
2x + 20
-2x - 2
--------
18

The result of the division is x^2 - 9x - 20, the quadratic polynomial.

Now, since we divided f(x) by (x + 1), we know that (x + 1) is a factor of the original polynomial. Therefore, the zeros of f(x) can be found by setting the quadratic polynomial equal to zero:

x^2 - 9x - 20 = 0

Now we can use factoring or the quadratic formula to solve for the remaining zeros.

Factoring the quadratic equation:

(x - 5)(x + 4) = 0

From this, we can see that the other zeros are 5 and -4.

To find the sum of the other zeros, we add them together:

5 + (-4) = 1

So, the sum of the other zeros is 1.