SOLUTION: A polynomial f and a factor of f are given. Factor f completly. F(x) = x^3 - 3x^2 - 16x - 12 ; x-6

Algebra ->  Test -> SOLUTION: A polynomial f and a factor of f are given. Factor f completly. F(x) = x^3 - 3x^2 - 16x - 12 ; x-6      Log On


   

Question 682502: A polynomial f and a factor of f are given. Factor f completly.
F(x) = x^3 - 3x^2 - 16x - 12 ; x-6
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Divide
%28x%5E3-3x%5E2-16x-12%29%2F%28x-6%29
...
(x-6) goes into x%5E3-3x%5E2 : x%5E2
to get
x%5E3+-+6x%5E2
subtracting
x%5E3+-+x%5E3+-+3x%5E2+-+-6x%5E2
yielding
3x%5E2
...
(x-6) goes into 3x%5E2+-+16x : 3x
to get
3x%5E2+-+18x
subtracting
3x%5E2+-+3x%5E2+-+16x+-+-18x
yielding
2x
...
(x-6) goes into 2x - 12: 2
to get
2x - 12
subtracting
2x - 2x - 12 - -12
yielding
0
...
%28x%5E3+-+3x%5E2+-+16x-12%29%2F%28x-6%29+=+x%5E2%2B3x%2B2
...
(x-6)(x^2+3x+2)
highlight_green%28f%28x%29=%28x-6%29%28x%2B2%29%28x%2B1%29%29
0 = x-6, highlight_green%28x+=+6%29 AND
0 = x+2, highlight_green%28x+=+-2%29 AND
0 = x+1, highlight_green%28x+=+-1%29
.....................
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