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If f(x) = x^3 - 6x^2 + 13x - 10, and x - 2x - 2 is a factor of f(x), then find all of the zeros of f(x) algebraically.

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Final answer:

To find the zeros of f(x) algebraically, divide f(x) by (x - 2) to get a quadratic equation. Solve the quadratic equation to find the zeros of f(x).

Step-by-step explanation:

To find the zeros of f(x) algebraically, we need to find the values of x that make f(x) equal to zero. Since x - 2 is a factor of f(x), we can use synthetic division or long division to find the other factor. Dividing f(x) by x - 2, we get a quotient of x^2 - 4x + 5. To find the zeros of this quadratic, we can set it equal to zero and solve for x. Using the quadratic formula, we get x = 2 ± √(-4 + 4) / 2 = 2 ± i.

Therefore, the zeros of f(x) are 2, 2 + i, and 2 - i.

User Eli Algranti
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