# How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^3-2x^2-5x+6#?

##### 1 Answer

See explanation...

#### Explanation:

Given:

#f(x) = x^3-2x^2-5x+6#

By the Rational Zeros theorem, any rational zeros of

That means that the only possible rational zeros are:

#+-1, +-2, +-3, +-6#

The pattern of signs of the coefficients of

The pattern of signs of the coefficients of

In addition, note that the sum of the coefficients of

#1-2-5+6 = 0#

Hence we can tell that

#x^3-2x^2-5x+6 = (x-1)(x^2-x-6) = (x-1)(x-3)(x+2)#

So the other two zeros of