SOLUTION: Divide using the synthetic method (x^5-6x^3+7x^2+10)/(x+3) ^ is suppose to mean an exponent

Question 723012: Divide using the synthetic method
(x^5-6x^3+7x^2+10)/(x+3) ^ is suppose to mean an exponent
Answer by 119078(26) (Show Source): You can put this solution on YOUR website!
Start by getting the problem set up
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x+3|x^5+x^4-6x^3+7x^2+x+10 There is a x^4 and x missing in the original problem. If you don't put it in when you are solving you will get it ALL wrong.
Next, how many more x's would you need to multiply to x to be x^5? x^4. So that is the first part of your problem. You then multiply (x*x^4) and then 3*x^4 which gives you (x^5+3x^4). Subtract that to
x^4
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x+3|x^5+x^4-6x^3+7x^2+x+10
-(x^5+3x^4)
0 -2x^4-6x^3 Then bring down
What times x would give you -2x^4? -2x^3. (x*-2x^3)+(3*-2x^3)= (-2x^4-6x^3). Subtract (-6y^2-30y) to (-6y^2-33y).
x^4-2x^3
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x+3|x^5+x^4-6x^3+7x^2+x+10
-(x^5+3x^4)
0 -2x^4-6x^3
-(-2x^4-6x^3)
0 0 -7^2 Then bring down
what times x gives you 0? 0 just as you were thinking! so for the last time multiply 0 to x and then 0 to 3. This will give you (0+0), subtract that to (0+7x^2).
x^4-2x^3+0x^2
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x+3|x^5+x^4-6x^3+7x^2+x+10
-(x^5+3x^4)
0 -2x^4-6x^3
-(-2x^4-6x^3)
0 0x^3+7x^2
-(0x^3+0x^2)
+7x^2+x Then bring down x
Now you keep this up until you get to the end. which will look like this:
x^4-2x^3+0x^2+7x-20
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x+3|x^5+x^4-6x^3+7x^2+x+10
-(x^5+3x^4)
0 -2x^4-6x^3
-(-2x^4-6x^3)
0 0x^3+7x^2
-(0x^3+0x^2)
7x^2+x
-(7x^2+21x)
0 -20x+10
-(-20x-60)
70
Answer all nice and pretty:

Because 0x^2=0 there is no point in having it in your final equation but if you would like you can.
I hope my step by step will help you get threw more problems like this. Yes it takes a long time to get these kind of problems done but it is all worth it in the end, because then you don't have to do it anymore! Have fun with the rest of your math!
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