If f(x)=x^3-4x^2-25x+28f(x)=x 3 −4x 2 −25x+28 and x-7x−7 is a factor of f(x)f(x), then find all of the zeros of f(x)f(x) algebraically.

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  x = {7, 1, -4}

Step-by-step explanation:

Dividing the given factor from the polynomial using synthetic division, we get ...

  f(x) = (x -7)(x^2 +3x -4)

Factoring the quadratic* gives ...

  f(x) = (x -7)(x -1)(x +4)

The zeros are the values of x that make these factors be zero:

  x = {7, 1, -4}

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* The constants in the binomial factors are factors of -4 that have a sum of +3. Those are (-1)(4) = -4. -1+4 = 3.