Factoring Problem: Solving x(xsquared-1)(xsquared-1)=0

[DethRose]

Hi

I have been working on this factoring problem for a while and don't 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 don't understand how you can get these answers by using the root of 1.

Any help is appreciated

thanks

 

[arildno]

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

 

[DethRose]

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

 

[Hootenanny]

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

 

[DethRose]

i see where you get that from but i don't understand why your allowed to do that

 

[arildno]

i see where you get that from but i don't understand why your allowed to do that

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!

 

[DethRose]

ok well i understand how you get the 1,-1 but i don't understand why the 0 is an answer as well

 

[arildno]

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

 

[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?

 

[arildno]

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

 

[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?

 

[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.

 

[DethRose]

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

 

[arildno]

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

Glad to be of help.

 

[Robokapp]

All you need to know is in order to pull out a zero from nothing but multiplications you need to multiply by zero somewhere.