use the rational zeros theorem to find all the real zeros of the polynomial function, use the zeros to factor f over the real numbers f(x)=x^3-x^2-37x-35

answer must use radical as needed and intergers or fractions

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Factor `f(x)=x^3-x^2-37x-35` :

The possible rational roots are `+-1,+-5,+-7,+-35`

We can use the root theorem to find a root:

`f(-1)=-1-1+37-35=0` so -1 is a root. We can use synthetic division or polynomial long division to find:

`x^3-x^2-37x-35=(x+1)(x^2-2x-35)`

The second factor can be factored as `(x-7)(x+5)`

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`x^3-x^2-37x-35=(x+1)(x-7)(x+5)`

The real zeros are -1,-5,7

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