Question 534459
List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial below and factor completely. Please show all of your work.
f(x) = 3x^4+17x^3+17x^2-33x-36
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Use Rational Roots Theorem to find real zeros:

....0...|......3........17.......17........-33.......-36..............
....1...|......3........20.......37..........4.........-32.......
....2...|......3........23.......63.........93.........150 (2 is upper limit), (root between 1 & 2)
.........................................................
....0...|......3........17.......17........-33.......-36
..-1...|......3........14........3.........-36........ 0 (-1 is a root)
.........................................................
....0...|......3........14........3.........-36
....1...|......3........17.......20........-16...................
....2...|......3........20.......43.........50 (2 is upper limit), (root between 1 & 2)
.........................................................
....0...|......3........14........3.........-36
..-1...|......3........11......-8.........-28..................
..-2...|......3.........8.......-13.......-10....................
..-3...|......3.........5.......-12..........0 (-3 is a root)
f(x)=(x+1)(x+3)(3x^2+5x-12)
f(x)=(x+1)(x+3)(3x-4)(x+3)
Zeros are:-3(multiplicity 2), -1, and 4/3
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Possible Rational Roots: p=factors of 36 (constant), q=factors of 3(lead coefficient)
...q\p...|..±1........±2.......±3.....±4......±6......±9.....±12.......±18.........±36.
...±1....|..±1.........±2......±3.....±4......±6......±9.....±12........±18.........±36   
...±3....|..±1/3....±2/3...........±4/3.......................................................±12