How Do I Solve Polynomial Division and Trigonometric Identities?

[Jimmy84]

Homework Statement

I forgot how to divide this

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

I don't know how to start since 3 has nothing to do with x^2.
The result from the book is 5 - x.


I also don't 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 don't 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 ?

Homework Equations

The Attempt at a Solution

Thanks in advance.

 

[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}.

 

[iRaid]

First 1 try synthetic division:
http://www.purplemath.com/modules/synthdiv.htm

 

[Jimmy84]

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

 

[Mark44]

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

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