- #1
mathdad
- 1,283
- 1
Factor
(x^2 + 1)^(3/2) + (x^2 + 1)^(7/2)
Solution:
(x^2 + 1)^(3/2)[1 + (x^2 + 1)^(7/12)]
Correct?
(x^2 + 1)^(3/2) + (x^2 + 1)^(7/2)
Solution:
(x^2 + 1)^(3/2)[1 + (x^2 + 1)^(7/12)]
Correct?
RTCNTC said:(x^2 + 1)^(3/2)(1 + (x^2 + 1)^2)
What about simplifying the right expression more?
Right Expression:
1 + (x^2 + 1)^2
1 + (x^2 + 1)(x^2 + 1)
1 + x^4 + 2x^2 + 1
x^4 + 2x^2 + 1
Factoring is the process of finding the factors, or numbers that can divide evenly into a given number. It is a fundamental concept in mathematics and is often used in algebra and number theory.
To factor a number, you need to find all of its factors. This can be done by listing out all the numbers that can divide evenly into the given number, and then identifying which of those numbers are the smallest possible factors. For larger numbers, there are various methods and techniques that can be used to factor them efficiently.
Factoring can be used to simplify and solve mathematical expressions, equations, and problems. It is also used in cryptography and coding theory to break down and analyze complex algorithms.
A prime number is a number that has only two factors: 1 and itself. On the other hand, a composite number has more than two factors. This means that a composite number can be broken down into smaller factors, while a prime number cannot.
Yes, factoring has several real-world applications. For example, it is used in finance to calculate interest rates, in chemistry to determine the molecular structure of compounds, and in computer science to optimize algorithms. It is also used in everyday life, such as finding the best deal when comparison shopping or calculating the dimensions of a room for remodeling.