Introduction
When dealing with algebraic expressions, one common task is to factorize them into their simplest form. In this article, we will explore the factors of the expression M^2 – 12M + 20. By factoring this expression, we can break it down into its constituent parts to better understand its behavior and properties. Let’s delve into the factors of this algebraic expression.
Finding Factors of M^2 – 12M + 20
To factorize an expression like M^2 – 12M + 20, we need to determine what values of M make the expression equal to zero. By finding these values, we can then find the factors of the expression. Let’s break down the process of factorizing the expression step by step.
Finding the Factors
First, let’s write the expression as follows: M^2 – 12M + 20 = 0. To factorize this expression, we need to find two numbers that multiply to 20 and add up to -12. These numbers are the factors of the given expression. Let’s explore how to find these factors.
Step 1
Identify the coefficient of M^2, which is 1 in this case. This represents the number that multiplies with M^2. In our expression M^2 – 12M + 20 = 0, the coefficient of M^2 is 1.
Step 2
Identify the constant term, which is the term without M or any variable attached. In our expression, the constant term is 20.
Step 3
Find the factors of the constant term 20. These factors are the numbers that multiply to give 20. For 20, the factors are:
- 1 and 20
- 2 and 10
- 4 and 5
Step 4
Among the factors of 20, find the pair that adds up to the coefficient of M, which is -12 in our expression. In this case, the pair that adds up to -12 is -2 and -10. These are the factors of the given expression M^2 – 12M + 20 = 0.
Factored Form
Using the factors we found, we can now express the given expression M^2 – 12M + 20 in its factored form. Since -2 and -10 are the factors that add up to -12 and multiply to 20, we can write the factored form as follows:
M^2 – 12M + 20 = (M – 2)(M – 10) = 0
This factored form represents the expression broken down into two parts, (M – 2) and (M – 10). These factors make up the original expression and help us understand it better.
Conclusion
In conclusion, the factors of the expression M^2 – 12M + 20 are (M – 2) and (M – 10). By finding the factors of an algebraic expression, we can simplify it and understand its properties more clearly. The process of factoring involves breaking down the expression into its constituent parts, making it easier to work with and analyze. Understanding factors is essential in algebra and mathematics as they help in solving equations and understanding relationships between variables.
