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dranseth
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Homework Statement
Factor the following over the set of rational numbers. Simplify if possible.
cos³ x-1
I do not know how to deal with the cubic cosine. Help is greatly appreciated.
dranseth said:so what you are saying is: Cos³ x-1 = cos(x-1)³ = (cosx-cos1)(cosx-cos1)(cosx-cos1)
Factoring over the set of rational numbers means finding the rational number factors of an expression. This involves breaking down the expression into smaller parts that can be multiplied together to get the original expression.
Factoring over the set of rational numbers is important because it helps simplify complicated expressions and equations. This can make solving problems and finding solutions much easier and more efficient.
To factor an expression over the set of rational numbers, you can use various techniques such as finding common factors, using the distributive property, or using the quadratic formula. It also helps to have a good understanding of the rules of fractions and rational numbers.
No, not all expressions can be factored over the set of rational numbers. Some expressions may have irrational or imaginary solutions that cannot be represented as rational numbers. In these cases, other methods must be used to solve the expression.
One strategy for factoring over the set of rational numbers is to start by finding common factors and then using the distributive property to break down the expression further. It can also be helpful to practice and familiarize yourself with different factoring techniques and to check your work by multiplying the factors back together to ensure you have factored correctly.