Question

Divide.

(6x^2+36x+35)/(x+5)

Your answer should give the quotient and the remainder.

Answer 1

`6x+6+(5)/(x+5)`

Explanation:

When we divide polynomials by polynomials with more than one term, we use long division or factorization to simplify.

This polynomial isn't easily divided after factorization so we will use long division. And we will use the remainder theorem to write any remainder.

`((6x^2+36x+35))/((x+5))`

We start long division by finding what multiplies with x+5 to get
`6x^2+36x`. This is 6x.

So
`6x(x+5)=6x^2+30x`. We have 6x left as a remainder from 36x.

We now divide x+5 into 6x+35. What multiplies with x+5 to get 6x+35? 6.

So we have 6x+6 as our answer so far and after we multiply 6(x+5)=6x+30 we will have a final remainder of 5.

We write our answer as
`6x+6+(5)/(x+5)`.