Question 183030
Find all rational zeros of the polynomial (using synthetic division)
22. p(x)= {{{x^4-2x^3-3x^2+8x-4}}}

What I did: multiples of 1= +-1 
            multiples of 4= +-1 +-4 +-2
possible zeros: +-1 +-4 +-2 (after dividing constant over leading coeficient)
I used synthetic division to test which are zeros. +1 worked, +4 did not, +2 using the quotient of +1 (1 -1 -4 4) did not work gave me remainder of 8, but when I used the original coeficients (1 -2 -3 8 -4)it gave me a zero. I was told by my professor that either way it should work. 
---------------------------------------------------
Since the coefficients add up to zero, x = 1 is a zero.

1)....1....-2....-3....8....-4
.......1....-1....-4...4..|..0

Since the quotient coefficients add up to zero. x = 1 is AGAIN a zero.

1)....1....-1....-4....4
.......1.....0....-4...|..0

Now you have a quadratic which says x^2-4 = 0
Factor to get (x-2)(x+2)=0
x = 2 or x = -2
-------------------------
The 4 zeros are 1,1,2,-2
============================
Cheers,
Stan H.