Question

How do you use synthetic division to divide `(x^2 + 13x + 40) ÷ (x + 8)`?

Answer 1

Doing synthetic division is rather like doing long division.

First look for a multiplier for `(x+8)` that will match the highest term `x^2`. That multiplier must be `x`:

`x(x+8) = x^2+8x`

Subtract the right hand side from the original `x^2+13x+40` to find the remainder:

`(x^2+13x+40)-(x^2+8x) = 5x+40`

Now look for a multiplier for `(x+8)` that will match the highest remaining term `5x`. That multiplier must be `5`:

`5(x+8) = 5x+40`

Subtract the right hand side from our last remainder `5x+40` to find the remainder:

`(5x+40)-(5x+40)=0`

Bingo! It divides perfectly.

Adding together the multipliers `x` and `5` that we found we get

`(x^2+13x+40)-:(x+8) = x+5`