Question

synthetic division (x3 - 7x2 + 8 ) ÷ (x + 1)

Answer 1

Hey, @daniellenicholexoxo, welcome to OpenStudy!

Have you done synthetic division before?

Answer 2

You would have to write down the solution of x+1=0, (which is -1) together with the coefficients of x³ - 7x² + 8 , (which are 1, -7 and 8) in the following way:

-1 | 1 -7 8
|
------------ +
1

Drop the first coefficient, 1, below the dotted line.

Answer 3

Now take the 1 below the dotted line and multiply it with the -1. Put the result below the -7 and add:

-1 | 1 -7 8
| -1
------------ +
1 -8

Answer 4

Oops, just in time to correct an error:

-1 | 1 -7 0 8
| -1
---------------- +
1 -8

I inserted a 0, because that is the coefficient of x: you had 1x³-7x²+0x+8

Answer 5

Now multiply -8 and -1 and put the result in the next column. Add:

-1 | 1 -7 0 8
| -1 8
---------------- +
1 -8 8

Do it again:

-1 | 1 -7 0 8
| -1 8 -8
---------------- +
1 -8 8 0

So the synthetic division has succeeded: the last 0 means there is no remainder.

The other numbers, 1, -8 and 8 are the coefficients of the quotient:

(x³ - 7x² + 8 ) ÷ (x + 1) = x² - 8x + 8