# How do you find all rational zeroes of the function using synthetic division #f(x)=2x^5+x^4-23x-16#?

##### 1 Answer

#### Explanation:

Given:

#f(x) = 2x^5+x^4-23x-16#

By Descartes' Rule of Signs

By the rational roots theorem, any rational zeros of

That means that the only possible rational zeros are:

#+-1/2, +-1, +-2, +-4, +-8, +-16#

We find:

#f(-2) = -64+16+46-16 = -18 < 0#

#f(-1) = -2+1+23-16 = 6 > 0#

#f(-1/2) = -1/16+1/16+23/2-16 = -9/2 < 0#

#f(1) = 2+1-23-16 = -36 < 0#

#f(2) = 64+16-46-16 = 18 > 0#

Hence

The remaining

We cannot immediately deduce it from what we have found, but actually none of the zeros are expressible in terms of