Rational Zeros
posted by JB on .
List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor
f(x)=2x^4+19x^3+37x^255x75

I tried ±1, ±3, ±5
found 1 and 5 to be zeros
So after synthetic division by x+1 and x+5
I got
2x^4+19x^3+37x^255x75 = (x+1)x+5)(2x^2 + 7x  15)
= (x+1)(x+5)(x+5)(2x  3)
so we have a double zero at 5, and zeros at 1 and 3/2 
any possible rational zeroes would have a numerator which divides 75 and a denominator which divides 2. So, the list would be
±1 ±3 ±5 ±15 ±25 ±75
±1/2 ±3/2 ±5/2 ±15/2 ±25/2 ±75/2 
DERRRR