Factoring Problem

1. Oct 10, 2006

DethRose

Hi

I have been working on this factoring problem for a while and dont understand how to get the answer.

The question is:

x(xsquared-1)(xsquared-1)=0

The answer that is in the back of the book is x=0,1 but i dont understand how you can get these answers by using the root of 1.

Any help is appreciated

thanks

2. Oct 10, 2006

arildno

You do mean the solutions being x=0, 1 and -1, right?

3. Oct 10, 2006

DethRose

yea i didnt know how to do the + ontop - thing but that works too lol

4. Oct 10, 2006

Hootenanny

Staff Emeritus
Okay so you have x(x2-1)(x2-1)=0. Now, this question can be solved by inspection. Remember that if you multiply any number by zero, then you obtain zero. So for the above equation this allows us to write:

x=0

or

(x2-1)=0

Can you see why?

Edit: Sorry Slow typist

5. Oct 10, 2006

DethRose

i see where you get that from but i dont understand why your allowed to do that

6. Oct 10, 2006

arildno

Allowed to do what?

Do not be a mysterious oracle whose meaning we need to figure out on your own. We are simple people here!

7. Oct 10, 2006

DethRose

ok well i understand how you get the 1,-1 but i dont understand why the 0 is an answer as well

8. Oct 10, 2006

arildno

Well, insert 0 at the x's place!
What is now the left-hand side of the equation.?
In particular, is it zero??

9. Oct 10, 2006

DethRose

ok i get what your saying there so say you get into a situation where the eqn is :

x(x+1)(x-1)(x+2)(x-2)

is the answer x= 1,-1,2,-2, and 0?

10. Oct 10, 2006

arildno

What you have written isn't an equation, it is an expression.
Please type in the equation you were thinking of!

11. Oct 10, 2006

DethRose

question is:

x(xsquared-1)(xsquared-4)=0
so i expanded to x(x+1)(x-1)(x+2)(x-2)=0

so i am wondering if the answer for that would be 1,-1,2,-2, and 0?

12. Oct 10, 2006

arildno

Precisely!

When any numbers (or expressions) are multiplied together, and the product is 0, then at least one of the factors has to be 0!

And whenever one of the factors IS zero, then the product must be zero.

13. Oct 10, 2006

DethRose

great...thanks for the helo you just helped me solve like 8 questions on my assignment

14. Oct 10, 2006