If x+2 is a factor, -2 is a zero. So we can put -2 in the left-hand corner of your synthetic division, bring the coefficients down so you'll have a set up like this:

-2 | 1 -3 -7

____________

1. bring down the 1:

-2 | 1 -3 -7

____________

2. multiply that by -2 and enter the result underneath 3:

-2 | 1 -3 -7

-2

___________

a. then, add through:

-2 | 1 -3 -7

-2

___________

1 -5

3. Do the same for -5 (multiply by the zero -2), enter that underneath -7 and add through:

-2 | 1 -3 -7

-2 10

___________

1 -5 3

Now, reassign the coefficients to their x. Because we already factored out an x with the zero, the 1 is assigned to 'x' rather than back to ' $x^{2}$ '. The '-5' will not have an x attached. '3' is your remainder and cannot be divided out any further, so it will be written as $\frac{3}{x+2}$ . Finally, just put them back together to get x-5+ $\frac{3}{x+2}$ .

Hope this helped!

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2 years ago