# How do you use the rational root theorem to find the roots of #8x^3-3x^2+5x+15#?

##### 2 Answers

#### Explanation:

The general form for a polynomial is as follows:

The rational roots theorem states that, to find any potential zeroes of a given polynomial function, the formula is:

Once you have all the potential zeroes of the function, you just have to test them using synthetic division.

You can't.

You can determine that

#### Explanation:

By the rational root theorem, any rational roots of

The prime factorisation of

The prime factorisation of

That means that the only possible rational roots are:

#+-1/8# ,#+-1/4# ,#+-3/8# ,#+-1/2# ,#+-5/8# ,#+-3/4# ,#+-1# ,#+-5/4# ,#+-3/2# ,#+-15/8# ,#+-5/2# ,#+-3# ,#+-15/4# ,#+-5# ,#+-15/2# ,#+-15#

That's quite a lot of possibilities to try, so let's narrow it down.

Let

Then

So we can deduce that

#f(-1) = -8-3-5+15 = -1#

#f(-3/4) = -8*3^3/4^3-3*3^2/4^2+5*3/4+15#

#= -27/8-27/16+15/4+15#

#= (-54-26+60+240)/16 = 220/16 = 55/4#

So