If f(x)=x^3-12x^2+35x-24f(x)=x 3 −12x 2 +35x−24 and f(8)=0f(8)=0, then find all of the zeros of f(x)f(x) algebraically.

The zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

Step-by-step explanation:

Given

Required

Find all zeros of the f(x)

If then:

And is a factor

Divide f(x) by x - 8

Expand the numerator

Rewrite as:

Factorize

Expand

Factorize

Multiply both sides by x - 8

Hence, the zeros of f(x) are: (x - 1), (x - 3) and (x - 8)

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