Question

Simplify using synthetic division: (n^2+7n+10)/(n+5)

Answer 1

So before we start our synthetic division, there is one thing that must be pointed out. Factors of a polynomial are given as (x-c1)(x-c2)(x-c3)....(x-cn)
What this means is that there MUST be a minus sign present. The only way for there to be a plus sign present is if the number c is actually negative. For example, you have an (n+5). What this means is you have actually (n-(-5)). So when we start our synthetic division, we must use the number -5. Now for the set up, we usually do some sort of column system. We use the factor number, -5 in our case, and the coefficient of every term in our polynomial. Now we must have a number for all power. So like if we had something like x^3 + x - 5, even though there is no x^2 term, we would have to place an x^2 term. Mainly by putting 0. But we dont have that here, I just thoughtId mention it. Now we set up our table using the -5 and all the coefficients of the polynomial liek so:

Answer 2

So from here, the first thing we do is drop the first number down, mainly the 1:


From here, we takr -5 and multiply it by this 1. The result will then go underneath the 7 like so: