# How do you find all the zeros of # f(x)=2x^3-13x^2+22x-8#?

##### 1 Answer

Apr 1, 2016

Use the Rational Factor Theorem to identify rational zeros.

#### Explanation:

According to the Rational Factor Theorem

if

they must be in the set

Evaluating the equation for each possibility:

identifies the zeros as#{color(red)(1/2),color(blue)(2),color(brown)(4)}#

which implies the factoring:

#color(white)("XXX")(color(red)(2x-1))(color(blue)(x-2))(color(brown)(x-4))#