What Are Algebraic Factors?
Algebraic factors are numbers, terms and/or arithmetic operations that divide exactly into another number, term or arithmetic operation. They can be used in algebra to solve or simplify algebraic expressions.
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Definition: A factor is a quantity that divides exactly into a term and is multiplied by something else to form that term. For example, 2 and x are factors of 2x and a, b and c are factors of abc.
Using these factors in algebra is called factoring. It is a common way to find the solutions of algebraic expressions and can be used to help us understand how math works.
The process of finding a factor in an expression is sometimes known as factoring, and it reverses the multiplication procedure that would be needed to multiply the expression. It can be used to find the prime factorization of a number or to figure out how to find the greatest common factor (GCF) of all of the terms in an expression.
When you first learn about factoring, it may seem a little confusing at first. However, once you understand the basic concepts and the steps involved in factoring, it is a very useful tool in mathematics.
1. Removing Common Factors.
To factor an expression, we must first remove any common factors that are present. Normally, only two terms are removed, but in some cases more than two can be found. In this case, we must use the distributive property to make sure that each of the new terms has a common factor.
2. The Greatest Common Factor.
The greatest common factor (GCF) of a term is the highest factor that can be taken commonly in the term. If we take the term 34xy + 17y, the GCF is 17y – 2.
3. The Reverse Distributive Property.
In algebra, the “reverse” distribute property is the process of rewriting each term as a product in order to factor it. This method is used to factor polynomials and trinomials, where the coefficients have degree three.
4. Grouping Problems.
When we want to factor a trinomial or a polynomial, the first step is to group the problem into smaller ones. There are several methods that can be used to do this. We will discuss each one in this section.
5. Reverse the Multiplication Table.
The easiest method for factoring an expression is to reverse the multiplication table. The key is to remember that we must always start with the largest number in the original expression. This is because if we start with the lowest number in the original expression, then we will get a factor that is larger than the rest of the term.
6. Grouping Trinomials.
For trinomials with degree 3, the easiest method to factor them is to group them into small groups. This can be done by using the distributive property and a set of parentheses.
The next step in factoring a trinomial is to determine whether or not the trinomial can be rewritten into a binomial expression. If it can, then we will use the binomial factoring method to find the remaining trinomial’s factors. This method is very similar to the factoring by grouping technique that we learned in the previous chapter.