# Thread: Use the given zero to find all the zeros of the function

1. ## Use the given zero to find all the zeros of the function

Use the given zero to find all the zeros of the function.
f(x) = x^3 + x^2 + 9x + 9
Given zero: r = 3i

So, I think that I have to use synthetic division using 3i and -3i as roots?
Is this right? If so, what is the next step?

2. Originally Posted by tsmith
Use the given zero to find all the zeros of the function.
f(x) = x^3 + x^2 + 9x + 9
Given zero: r = 3i

So, I think that I have to use synthetic division using 3i and -3i as roots?
Is this right? If so, what is the next step?
Since two of the zeros are 3i and -3i you can multiply their linear parts like so:

(x-3i)(x+3i)=x^2+6i-6i-9(i^2)=
x^2+9

Now synthetically divide f(x) by x^2+9 and you should get your last zero solution.

3. Originally Posted by tsmith
Use the given zero to find all the zeros of the function.
f(x) = x^3 + x^2 + 9x + 9
Given zero: r = 3i

So, I think that I have to use synthetic division using 3i and -3i as roots?
Is this right? If so, what is the next step?
The bold is correct. So you just need one more real root.
$(x^2+9)$ is is one factor.

4. factor: (x + 1)(x^2 + 9) = (x + 1)(x + 3i)(x - 3i),