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Answer: OPTION B
Step-by-step explanation:
You need to follow these steps:
- Carry the number 2 down and multiply it by the the number -3.
- Place the product obtained above the horizontal line, below the number 4 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number -3.
- Place the product obtained above the horizontal line, below the number -4 and add them.
- Put the sum below the horizontal line.
- Multiply this sum by the number -3.
- Place the product obtained above the horizontal line, below the number 6 and add them.
Then:
[tex]-3\ |\ 2\ \ \ \ \ 4\ \ -4\ \ \ \ \ \ 6\\\.\ \ \ \ \ |\ \ \ \ -6\ \ \ \ \ 6\ \ \ -6[/tex]
[tex]-----------------[/tex]
[tex].\ \ \ \ \ \ 2\ \ \ -2\ \ \ \ 2\ \ \ \ \ 0[/tex]
Therefore, the quotient in polynomial form is:
[tex]2x^2-2x+2[/tex]
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Rewritten by : Barada
Answer:
B
Step-by-step explanation:
This was originally a third degree polynomial:
[tex]2x^3+4x^2-4x+6[/tex], to be exact.
When you divide by -3, you are basically trying to determine if x + 3 is a zero of that third degree polynomial. The quotient is always one degree lesser than the polynomial you started with, and if there is no remainder, then x + 3 is a zero of the polynomial and you could go on to factor the second degree polynoial completely to get all 3 solutions. To perform the synthetic division, you always first bring down the number in the first position, in our case a 2. Then multiply that 2 by -3 to get -6.
-3| 2 4 -4 6
-6
2 -2
So far this is what we have done. Now we multiply the -3 by the -2 and put that up under the -4 and add:
-3| 2 4 -4 6
-6 6
2 -2 2
Now we multiply the -3 by the 2 to get -6 and put that up under the 6 and add:
-3| 2 4 -4 6
-6 6 -6
2 -2 2 0
That last row gives us the depressed polynomial, which as stated earlier here, is one degree less than what you started with:
[tex]2x^2-2x+2[/tex]
