SOLUTION: 18x^3-36x^2-38x-4 / 6x+4

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Question 266642: 18x^3-36x^2-38x-4 / 6x+4
Answer by drk(1908) About Me  (Show Source):
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We can solve this by polynomial or synthetic division. Synthetic is faster. First, set 6x + 4 = 0 and solve for x as x = -2/3. Now divide as
(-2/3) // . . . . . . . . 18 . . . . . . -36. . . . . . -38 . . . . . . . -4
. . . . . . . . . . . . . . . . . . . . . . . . -12 . . . . . . 32 . . . . . . . . 4
. . . . . . . . . . . . . . . .18. . . . . . . -48. . . . . . .-6. . . . . . . . .0
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we know one root is x = (-2/3)
we have
18x^2 - 48x - 6 = 0
divide by 6 to get
3x^2 - 8x - 1 = 0
using the quadratic, we get
x ~ 2.786
and
x ~ -0.1196
so, our 3 roots are
{-2/3, -.1196, and 2.786}