# What are the possible integral zeros of #P(y)=y^4-5y^3-7y^2+21y+4#?

##### 1 Answer

Jan 11, 2017

The "possible" integral zeros are

None of these work, so

#### Explanation:

#P(y) = y^4-5y^3-7y^2+21y+4#

By the rational root theorem, any rational zeros of

That means that the only possible rational zeros are the possible integer zeros:

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

Trying each of these, we find:

#P(1) = 1-5-7+21+4 = 14#

#P(-1) = 1+5-7-21+4 = -18#

#P(2) = 16-40-28+42+4 = -6#

#P(-2) = 16+40-28-42+4 = -10#

#P(4) = 256-320-112+84+4 = -88#

#P(-4) = 256+320-112-84+4 = 384#

So