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

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In summary, the conversation revolves around a factoring problem where the equation x(xsquared-1)(xsquared-1)=0 needs to be solved. The solutions are x=0, 1 and -1, and the process involves writing the equation in the form of x=0 or (xsquared-1)=0. The conversation also discusses a similar equation, x(x+1)(x-1)(x+2)(x-2)=0, and concludes that the solutions are 1,-1,2,-2, and 0. The key concept is that whenever a product is equal to 0, at least one of the factors must also be 0.
  • #1
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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  • #2
You do mean the solutions being x=0, 1 and -1, right?
 
  • #3
yea i didnt know how to do the + ontop - thing but that works too lol
 
  • #4
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
i see where you get that from but i don't understand why your allowed to do that
 
  • #6
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!
 
  • #7
ok well i understand how you get the 1,-1 but i don't understand why the 0 is an answer as well
 
  • #8
Well, insert 0 at the x's place!
What is now the left-hand side of the equation.?
In particular, is it zero??
 
  • #9
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.
 

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

1. What is factoring and why is it important in solving equations?

Factoring is the process of breaking down a mathematical expression into smaller parts. It is important in solving equations because it allows us to rewrite complex expressions into simpler forms, making them easier to solve.

2. How do I know when to use factoring to solve an equation?

You can use factoring when an equation is in the form of a polynomial, where the highest exponent is 2 or higher. In this case, factoring can help you find the solutions to the equation.

3. What are the steps to factoring a quadratic equation?

Step 1: Check if the equation is in the form of ax2 + bx + c = 0.
Step 2: Find the factors of a and c.
Step 3: Rewrite the middle term bx as the sum of two terms using the factors found in step 2.
Step 4: Group the terms and factor by grouping.
Step 5: Set each factor equal to 0 and solve for x.
Step 6: Check the solutions by plugging them back into the original equation.

4. How does factoring help in solving a quadratic equation?

Factoring helps in solving a quadratic equation by breaking it down into simpler expressions, making it easier to find the solutions. It also helps in identifying patterns and relationships between numbers, which can lead to quicker solutions.

5. Can you give an example of solving the factoring problem: x(xsquared-1)(xsquared-1)=0?

Step 1: Check that the equation is in the form of ax2 + bx + c = 0.
Step 2: Find the factors of a and c. In this case, a = 1 and c = 0.
Step 3: Rewrite the middle term bx as the sum of two terms using the factors found in step 2.
Thus, x(xsquared) can be rewritten as x(xsquared-1).
Step 4: Group the terms and factor by grouping.
x(xsquared-1) can be factored as x(xsquared-1)(xsquared-1)=0
Step 5: Set each factor equal to 0 and solve for x.
Thus, x=0 or xsquared-1=0. Solving for xsquared, we get xsquared=1. Therefore, the solutions are x=0, x=1, and x=-1.
Step 6: Check the solutions by plugging them back into the original equation.
When x=0, the equation becomes 0(0)(0-1)(0-1)=0, which is true. Similarly, for x=1 and x=-1, the equation holds true.

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