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So before we start our synthetic division, there is one thing that must be pointed out. Factors of a polynomial are given as (x-c1)(x-c2)(x-c3)....(x-cn) What this means is that there MUST be a minus sign present. The only way for there to be a plus sign present is if the number c is actually negative. For example, you have an (n+5). What this means is you have actually (n-(-5)). So when we start our synthetic division, we must use the number -5. Now for the set up, we usually do some sort of column system. We use the factor number, -5 in our case, and the coefficient of every term in our polynomial. Now we must have a number for all power. So like if we had something like x^3 + x - 5, even though there is no x^2 term, we would have to place an x^2 term. Mainly by putting 0. But we dont have that here, I just thoughtId mention it. Now we set up our table using the -5 and all the coefficients of the polynomial liek so: |dw:1378167006138:dw|
So from here, the first thing we do is drop the first number down, mainly the 1: |dw:1378167055314:dw| From here, we takr -5 and multiply it by this 1. The result will then go underneath the 7 like so: |dw:1378167088301:dw|
The next step from here is to add the numbers in that second column. SO we have a 7 + a -5. This makes 2. This 2 will drop down to the bottom of the column: |dw:1378167138018:dw| Now as before, what we have on the bottom of the column is multiplied by the -5 we have. So now Ill multiply -5 and 2 and place it under the 10 in the next column. |dw:1378167178753:dw| Now just following in order of our steps, I added the two numbers in the last column and came up with 0. So now the only thing to do is look at all the numbers we have at the bottom of our columns.
So we have a 1, 2, and a 0. The 0 does not matter for us right here. If the number were not a 0, we would havea remainder to worry about, but in this case we don't. So the 1 and the 2 represent thwecoefficients of our answer. Now, our beginning polynomial had a degree of 2. SO our answer must have a degree 1 less than that. This means that the 1 represents the coefficient of x^1 and the number 2 is simply a number. this means our final answer is (x + 2) Make sense?
It does make sense. I think I understand it now. Thank you!
Okay, awesome ^_^