# What is the factoring by grouping? When factoring a trinomial, why is it necessary to write the trinomials in four terms?

I will be happy to critique your thinking on this.

I do not understand to even answer it?

How do we determine the common factors in an expression? Also When factoring a trinomial, why is it necessary to write the trinomials in four terms

## Factoring by grouping is a technique used to factorize a polynomial expression by grouping its terms in a specific way. To understand why it is necessary to write a trinomial in four terms, let's start with determining common factors in an expression.

To determine common factors in an expression, you need to analyze the terms and identify any common factors they might have. A common factor is a term that can be divided evenly into each term of the expression without leaving a remainder. For example, in the expression 2x + 4x, the common factor is 2x. In the expression 3xy + 9x, the common factor is 3x.

When it comes to factoring a trinomial, it is necessary to write the trinomials in four terms because sometimes the common factors are not immediately apparent. By expanding the trinomial into four terms, we expose potential common factors that might not be apparent in its original form. Rearranging the trinomial into four terms allows us to group the terms in a way that simplifies the factoring process.

The four-term expression can be written as (ax + bx) + (cx + dx), or we can regroup the terms as (ax + cx) + (bx + dx), where a, b, c, and d are coefficients or constants.

Once the trinomial is written in four terms, we can group the terms in pairs and search for any common factors between the pairs. By factoring out these common factors from each pair, we can then further manipulate the expression to obtain the final factored form.

Overall, the process of factoring by grouping in four terms is a systematic approach that helps identify and factor out any common factors from a trinomial expression. It simplifies the factoring process by breaking down the expression into smaller, more manageable parts, making it easier to find the factors that are common between the terms.