Question

X² – 3x-7 x+2 Divide the following using synthetic division

Answer 1

Answer:

x-5+ $\frac{3}{x+2}$

Step-by-step explanation:

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

____________

       1

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

-2 |   1    -3    -7

             -2

___________

       1

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!