## Algebra and Functions

## Simplifying algebraic fractions

## Dividing polynomials by (x ± p)

The key here is to remember how to use

A polynomial is a set of positive powers in order

**long division**all the way back in**primary school**!!A polynomial is a set of positive powers in order

If you can't follow the diagram this video takes you through the process step by step -http://www.youtube.com/watch?v=qIpCI2iKbAg |

If at the end a number is left over then write it as a remainder

## Factor Theorem

The (x ± p) is generally a factor of the polynomial and the factor theorem enables you to find this factor as it is rarely provided

The factor theorem states:

This enables you to factorise a cubic.

The factor theorem states:

**If f(x) is a polynomial and f(p) = 0 the (x - p) is a factor of f(x)**This enables you to factorise a cubic.

In an exam you need to find out 'p' through

To factorise the cubic

This can then be further factorised giving three sets of brackets normally.

Also if f(x) is a polynomial and

**trial and error**until the value brings it to 0. Remember p can be**+ve**and**-ve**To factorise the cubic

**fully**divide the cubic by the factor found which will give a quadratic.This can then be further factorised giving three sets of brackets normally.

Also if f(x) is a polynomial and

__f(b/a)=0__then**is a factor**__(ax + b)__## Remainder Theorem

To find the remainder without using long devision (or to check the long devision) you can use the remainder theorem

The remainder theorem states:

The remainder theorem states:

**If a polynomial f(x) is divided by (ax - b) then the remainder is f(b/a)**