Hello, I need some help solving this problem, please! The exact directions are..

Question

Hello, I need some help solving this problem, please!
The exact directions are...
Given the polynomial F(x) = x^3 - 6x^2 + 13x - 10 (hint: userational zeros test. The given f(x) has a complex root(s) also)
a) Find all the zeros of F(x)
b) Write them as a product of linear factors.

This is the progress I've made...
a) Zeros of F(x): x = 2 (when y = 0), then I used the quadraticformula to get 2 +/- i for the second and third zeros of F(x).
b) Product of linear factors: (x - 2) [x - (2 + i)] [x - (2-i)]

Am I missing any zeros of F(x)? Have I written the factorsout correctly to get credit for this question? Checking mywork: if I multiply the product of the linear factors will theyequal the original polynomial, F(x)?
Please, a full explanation of any errors I've made will help meunderstand how to complete this.

Thank you for your time!

Explanation / Answer

There is a simple way to see how many zeros (normal,complex, andrepeated) are in a function. You look at the highest power and thatis exactly how many zeros there are. So in your case, the highest power is x^3 meaning 3 solutions. The second thing I would note is that complex zeros always come incomplements. (2+i) and (2-i) are complements. Your answer is correct. Good job!

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