What is 26x – 5 factored
The Correct Answer and Explanation is :
To factor the expression (26x – 5), we can look for the greatest common factor (GCF) of the two terms. The two terms in this expression are (26x) and (-5).
- Identify the GCF: The coefficients are (26) and (-5). The GCF of (26) and (5) is (1), as (26) is not divisible by (5). Thus, the GCF we can factor out from the expression is (1).
- Rewrite the Expression: Since the GCF is (1), we can rewrite the expression as:
[
26x – 5 = 1(26x – 5)
] - Final Factored Form: The factored form of the expression (26x – 5) remains (26x – 5) because there are no common factors other than (1).
Explanation of the Process
Factoring is a crucial skill in algebra that allows us to simplify expressions and solve equations more easily. In this case, the expression (26x – 5) consists of a variable term ((26x)) and a constant term ((-5)). To factor it, we first identify the GCF of the coefficients, which is the largest number that can divide each term evenly.
If the GCF were greater than (1), we could factor it out to express the equation in a simpler form. For example, if we had (12x + 8), the GCF is (4), and we could rewrite it as (4(3x + 2)). However, in this case, since the GCF is (1), the expression cannot be simplified further through factoring.
Understanding how to factor expressions helps in various mathematical applications, including solving quadratic equations and simplifying polynomial expressions. It also forms the basis for more advanced topics, such as polynomial division and the application of the quadratic formula. Overall, being comfortable with factoring can enhance problem-solving skills in mathematics.