Factoring is the process of breaking down a mathematical expression into smaller parts, known as factors. It is used to simplify complex expressions and make them easier to work with.
Factoring is important because it allows us to solve equations, simplify expressions, and find common factors. It is also an important skill in algebra and is used in many real-world applications, such as calculating interest rates and solving engineering problems.
To factor a polynomial, you need to find its factors, which are numbers or expressions that can be multiplied together to get the original polynomial. The first step is to look for common factors and then use various factoring techniques, such as grouping, difference of squares, and perfect square trinomials, to factor the polynomial completely.
Factoring and expanding are opposite operations. Factoring breaks down an expression into smaller parts, while expanding combines smaller parts to form a larger expression. In other words, factoring is the reverse of expanding.
No, not all polynomials can be factored. Some polynomials, such as prime polynomials, cannot be broken down into smaller factors. However, every polynomial can be factored into a product of linear and quadratic factors, which may include imaginary numbers.