# A division and a problem

1. May 15, 2010

### Jimmy84

1. The problem statement, all variables and given/known data
I forgot how to divide this

1.) x^2 + 15 -8x divided by 3 - x

I dont know how to start since 3 has nothing to do with x^2.
The result from the book is 5 - x.

I also dont understand this problem which uses trigonometric identities.
if x = a sin theta then

2.) square rt of a^2 - x^2

= square rt of a^2 - a^2 sin^2 theta
= square rt of a^2 square rt of 1 - sin^2 theta
= a cos theta .

I dont understand why does

square rt of a^2 - a^2 sin^2 theta

= square rt of a^2 square rt of 1 - sin^2 theta ?

2. Relevant equations

3. The attempt at a solution

2. May 15, 2010

### Gib Z

1) When dividing, rewrite all the polynomials with highest power of x first, then decreasing powers of x from there.

2) Firstly, we can factor a^2-a^2 sin^2 theta as a^2( 1 - sin^2 theta).

Then we can break up the squareroot using $\sqrt{xy} = \sqrt{x} \sqrt{y}$.

3. May 15, 2010

### iRaid

4. May 15, 2010

### Jimmy84

Thanks by ordering the polynomials and using syntethic division I have 3 dividing 1 -8 +15 which equals x - 5 ?

5. May 16, 2010

### Staff: Mentor

No. Dividing x2 - 8x + 15 by 3 - x is equivalent to dividing -x2 + 8x - 15 by x - 3.