SOLUTION: Find all the rational zeros of the function f(x)=5x^4-15x^3-265^2-45x

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Question 1067432: Find all the rational zeros of the function f(x)=5x^4-15x^3-265^2-45x
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
5x^4-15x^3-265x^2-45x
factor out a 5x
5x(x^3-3x^2-53x-9)=0 notice I wrote 265x^2
x=0 is one root.
synthetic division
1===-3===-53===-9 try 9
1====6===1======0
(x-9)(x^2+6x+1)=0
x=9 is a second root
x=(1/2)(-6 +/- sqrt (36-4)); sqrt (32)=4 sqrt(2))
x=-3+/- 2 sqrt (2), the other two roots, numerically about -5.8 and -0.2
graph%28300%2C300%2C-8%2C11%2C-1200%2C1200%2C5x%5E4-15x%5E3-265x%5E2-45x%29
graph%28300%2C300%2C-2%2C2%2C-10%2C10%2C5x%5E4-15x%5E3-265x%5E2-45x%29