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

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The factoring problem x(xsquared-1)(xsquared-1)=0 can be solved by recognizing that if any factor equals zero, the entire product is zero. This leads to the solutions x=0, x=1, and x=-1. The discussion clarifies that inserting zero into the equation confirms it satisfies the condition for zero. Additionally, a related expression x(xsquared-1)(xsquared-4)=0 yields the solutions x=0, x=1, x=-1, x=2, and x=-2. Understanding that a product equals zero when at least one factor is zero is key to solving these types of equations.
DethRose
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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
 
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You do mean the solutions being x=0, 1 and -1, right?
 
yea i didnt know how to do the + ontop - thing but that works too lol
 
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
 
i see where you get that from but i don't understand why your allowed to do that
 
DethRose said:
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!
 
ok well i understand how you get the 1,-1 but i don't understand why the 0 is an answer as well
 
Well, insert 0 at the x's place!
What is now the left-hand side of the equation.?
In particular, is it zero??
 
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
What you have written isn't an equation, it is an expression.
Please type in the equation you were thinking of!
 
  • #11
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
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
great...thanks for the helo you just helped me solve like 8 questions on my assignment
 
  • #14
DethRose said:
great...thanks for the helo you just helped me solve like 8 questions on my assignment
Glad to be of help. :smile:
 
  • #15
All you need to know is in order to pull out a zero from nothing but multiplications you need to multiply by zero somewhere.
 

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