Find all the zeros of f(x). f(x) = x^4 - 4x^3 - 7x^2 + 28x Hint: First factor out an x, then get the p/q list.  List your answers from smallest to largest.  If there is a double root, list it twice.  Use a comma to separate answers.  Keep fractions in fractional form.  

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`f(x) = x^4 -4x^3 - 7x^2 + 28x`

`f(x) = x(x^3 -4x^2 - 7x +28)`

Break trinomial into groups: `(x^3-4x^2)` and `(-7x+28)`

` `Factor each: `x^2(x - 4)`  and `-7(x - 4)`

Since both have factor of (x - 4) combine the 2 and the original x that was factored to get:

`f(x) = x (x - 4) (x^2-7)`

To find zeros of f(x), set the function equal to zero.

`x (x - 4) ( x^2 - 7) = 0`

Set each factor equal to zero and solve for x.

1)  `x = 0`

2)  `x - 4 = 0 rArr x = 4`

3)  `x^2 - 7 = 0rArr x^2 = 7 rArr x =+-sqrt(7)` ` `

The zeros to the function are:  `0, 4,sqrt(7), -sqrt(7)`

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