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If f(x)=x³-4x²+6x+36 and x=2 is a factor of f(x), then find all of the zeros of f(x)?

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Final answer:

To find the zeros of f(x), divide f(x) by (x-2) using long division. The other factor will give the remaining zeros of f(x).

Step-by-step explanation:

To find the zeros of f(x), 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 long division to divide f(x) by (x-2) and find the other factor:

(x³-4x²+6x+36) ÷ (x-2)

After performing the division, we get a quotient of x²-2x-18.

To find the zeros of x²-2x-18, we can set it equal to zero and solve for x. We can factor the quadratic to (x-6)(x+3), so the zeros of f(x) are x=2, x=6, and x=-3.

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