SOLUTION: I need to use synthetic division to factor 3x^3-16x^2-72 into (x-6) and blank? I have no clue on how to do this or what the answer is. Can anyone help?

Question 57114: I need to use synthetic division to factor 3x^3-16x^2-72 into (x-6) and blank? I have no clue on how to do this or what the answer is. Can anyone help?
Found 2 solutions by stanbon, funmath:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I need to use synthetic division to factor 3x^3-16x^2-72 into (x-6) and blank?
--------------
6) 3 -16 0 -72
+18 +12 +72
-----------------------
3 +2 =12 | 0
This shows the factors are (x-6)(3x^2+2x-12)
Cheers,
Stan H.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
I need to use synthetic division to factor 3x^3-16x^2-72 into (x-6) and blank?
:
I have not been answering these division problems because I can't get the computer to show things in an easily understood way. I'll give it a try.
:
The coefficients in decending order of 3x^3-16x^2-72 are 3, -16, 0, -72. You need the 0 because there is no x, so it's understood coeffiecient is 0.
:
You put the opposite sign of -6 outside (from x-6) and the coeffiecints on the inside.
6|3 -16 0 -72
:|0
---------------Bring the 3 down:
::3
:
6|3 -16 0 -72
:|0 18
----------------Multiply 6 times the 3 you brought down and put that answer under the next coefficient.
::3
:
6|3 -16 0 -72
:|0 18
-----------------add -16+18 and write it under the line
::3 2
:
6|3 -16 0 -72
:|0 18 12
------------------Multiply 6 times 2 and put that answer under 0
::3 2
:
6|3 -16 0 -72
:|0 18 12
------------------Add 0+12 and write the answer under them.
::3 2 12
:
6|3 -16 0 -72
:|0 18 12 72
------------------Multiply 6 times 12 and put that under -72
::3 2 12
:
6|3 -16 0 -72
::|0 18 12 72
-------------------add -72 and 72 and put that answer under them
::3 2 12 0
:
Because the last column is 0, (x-6) is a factor of 3x^3-16x^2-72
If you look at the numbers under the line, that is the coefficients of the answer starting one degree less than where you started, 3.
3x^2+2x+12
therefore:
3x^3-16x^2-72=(x-6)(3x^2+2x+12)
I hope that you can decipher it.
Happy Calculating!!!
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