Question 89876
What are all the rational zeros of these polynomials?
y=2x^3-10x^2-8x+40 
I graphed it to find a zero at x=-2.
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Then used synthetic division as follows:
-2....2....-10....-8....40
........2.....-14....20..|..0

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Remainder: 0
Quotient: 2x^2-14x+20
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Find the zeroes of the Quotient:
2(x^2-7x+10)=0
x^2-7x+10=0
(x-5)(x-2)=0
x=5 or x=2
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and y=3x^3-24x^2-48x+384
Graphing shows a zero at x=-4
Use synthetic division to find the other two zeroes:
-4)....3....-24....-48....384
.........3.....-36....96...|..0
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Remainder: 0
Quotient: 3x^2-36x+96
Find the zeroes of the quotient:
3(x^2-12x+32)=0
x^2-12x+32=0
(x-4)(x-8)=0
x=4 or x=8
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Cheers,
Stan H.