# How do you use the rational root theorem to find the roots of # f(x) = x^3-4x^2-2x+8#?

##### 1 Answer

Use the rational root theorem to identify the possible rational roots to try. Hence find

#### Explanation:

#f(x) = x^3-4x^2-2x+8#

By the rational root theorem, any rational roots of

So the only possible rational roots are:

#+-1# ,#+-2# ,#+-4# ,#+-8#

#f(2) = 8-16-4+8 = -4#

#f(-2) = -8-16+4+8 = -12#

#f(4) = 64 - 64 - 8 + 8 = 0#

So

#x^3-4x^2-2x+8 = (x-4)(x^2-2)#

The remaining roots are the irrational roots of

#x = +-sqrt(2)#