Help me solve this problem that I missed, so that I can see where I went wrong. Synthetic Division
(3X3 -2x +5). (x-2)
I would set it up with the following algorithm to do synthetic division
(this is how I do it and how I taught it, the ----- are simply there to keep the columns lined up. The first 2 represents your divisor x-2, had it been x+5, I would have used -5. The 3 0 -2 5 are the coefficients of your polynomial)
2 │ 3 0 -2 5
------6 12 20
----3 6 10 25
I brought the 3 down two rows, multiply that first 3 times the number out front, 3x2=6,
I put the 5 under the 0 and added them to get 6.
Now multiply that 6 by the 2 to get 12, placing that 12 under the -2 and add them to get 1
Now 10 times the 2 etc to get 25
Now look at the last row: 3 6 10 25
Since you divided a cubic by a first degree, the answer should be a second degree expression
Your answer will be 3x^2 + 6x + 10 with a remainder of 25
The second line of my explanation has a typo
"I put the 5 under the 0 and added them to get 6"
should have been:
I put the 6 under the 0 and added them to get 6