- #1
pivoxa15
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Homework Statement
How does one know x^4+x^2+1=(x^2-x+1)(x^2+x+1)?
How does one get to that step?
I can find the roots of x but that doesn't seem to help. Is it be random trial and error?
Factoring involves systematically breaking down a number into smaller factors. While it may involve some trial and error, it is not completely random. There are specific rules and strategies that can be used to make the process more efficient and accurate.
Factoring is important in mathematics because it allows us to simplify and solve complex equations. It is also used in real-world applications such as cryptography and data compression.
No, not all numbers can be factored. Prime numbers, for example, can only be factored by themselves and one. However, most composite numbers can be factored into smaller prime numbers.
You have factored a number completely when there are no more common factors that can be divided out. This means that all of the factors are prime numbers and cannot be divided any further.
Factoring is the process of breaking down a number into smaller factors, while prime factorization is the process of finding the prime numbers that make up a given number. Prime factorization is a type of factoring, but not all factoring involves prime numbers.