You are Here: Home >< Maths

# What is the Factor Theorem? Watch

1. Can someone explain to me what the factor theorem is.

I heard that it something to do with :

If (x-3)=0, than f(3)=0
2. Let f(x) be a polynomial. The factor theorem tells us that (x - a) divides f(x) (as polynomials, not as numbers!) if and only if f(a) = 0. For example:
1. . f(1) = 0 and f(2) = 0, so (x - 1) and (x - 2) both divide f(x), and in fact as it turns out, f(x) = (x - 1)(x - 2).
2. . We notice that for any real number , , so no polynomial of the form (x - a) divides f(x) at all.

The factor theorem is a corollary of the remainder theorem.
3. (Original post by Zhen Lin)
Let f(x) be a polynomial. The factor theorem tells us that (x - a) divides f(x) (as polynomials, not as numbers!) if and only if f(a) = 0. For example:
1. . f(1) = 0 and f(2) = 0, so (x - 1) and (x - 2) both divide f(x), and in fact as it turns out, f(x) = (x - 1)(x - 2).
2. . We notice that for any real number , , so no polynomial of the form (x - a) divides f(x) at all.

The factor theorem is a corollary of the remainder theorem.
Well, considering you have a BA from Cam ill take ur wrd for it

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: December 20, 2010
Today on TSR

### Degrees to get rich!

... and the ones that won't

### Cambridge interviews pour in...

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.