Question

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

Answer 1

x-5+
`(3)/(x+2)`

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
`(3)/(x+2)`. Finally, just put them back together to get x-5+
`(3)/(x+2)`.

Hope this helped!