# How do you find all the zeros of #f(x)=x^4+5x^3+5x^2-5x-6#?

##### 1 Answer

Look at coefficient sums and divide by the factors found to simplify the problem and find zeros:

#x=1# ,#x=-1# ,#x=-2# and#x=-3#

#### Explanation:

First note that the sum of the coefficients is zero.

That is:

So

#x^4+5x^3+5x^2-5x-6 = (x-1)(x^3+6x^2+11x+6)#

Next note the if you reverse the signs of the terms of the remaining cubic factor with odd degree then the sum of the coefficients is zero.

That is

So

#x^3+6x^2+11x+6 = (x+1)(x^2+5x+6)#

Then note that

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

Putting this all together, we find:

#f(x) = (x-1)(x+1)(x+2)(x+3)#

with zeros