# Rational Zeros

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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^2-55x-75

• Rational Zeros -

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^2-55x-75 = (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

• Rational Zeros -

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

• Rational Zeros -

DERRRR

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