Factoring x^2 + 64: Is it Possible?

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In summary, factoring is the process of finding the factors or divisors of a number, which are numbers that can be multiplied together to get the original number. It is important in mathematics and has real-world applications. There are different methods of factoring depending on the type of expression. All numbers can be factored, but some may only have 1 and the number itself as factors. Factoring is also used in solving equations by simplifying and finding the roots or solutions.
  • #1
mathdad
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Factor x^2 + 64.

I say it cannot be factored because the expression is irreducible over integers.

Right?
 
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  • #2
RTCNTC said:
Factor x^2 + 64.

I say it cannot be factored because the expression is irreducible over integers.

Right?
Yeppers!

-Dan
 
  • #3
Cool.
 

FAQ: Factoring x^2 + 64: Is it Possible?

What is factoring?

Factoring is the process of finding the factors or divisors of a number. Factors are numbers that can be multiplied together to get the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Why is factoring important?

Factoring is important in many areas of mathematics, such as algebra and number theory. It is also used in real-world applications, such as finding the lowest common denominator in fractions and simplifying complex equations.

What are the different methods of factoring?

There are several different methods of factoring, including trial and error, grouping, difference of squares, and the quadratic formula. The method used depends on the type of expression being factored.

Can all numbers be factored?

Yes, all numbers can be factored. However, for some numbers, the only factors are 1 and the number itself. These numbers are called prime numbers. For example, 5 is a prime number because its only factors are 1 and 5.

How is factoring used in solving equations?

Factoring is used to simplify equations and make them easier to solve. It can also be used to find the roots or solutions of equations. By factoring, we can rewrite an equation in a way that makes it easier to find the value of the variable.

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