Factoring is a common algebraic process used to simplify expressions and solve equations. In order to find the factored form of 8X^2 – 12X, we need to identify common factors that can be factored out. Let’s delve into the details of factoring this expression.
Understanding Factoring in Algebra
Factoring is the process of breaking down an algebraic expression into simpler factors. This is done by finding common factors that can be factored out of a given expression. Factoring is important in algebra because it allows us to simplify expressions, solve equations, and make calculations easier.
Factored Form of 8X^2 – 12X
The expression 8X^2 – 12X can be factored by identifying common factors of the terms in the expression. In this case, both terms have a common factor of 4X. Let’s break down the factoring process step by step:
- Identify the common factor: The common factor of 8X^2 and 12X is 4X.
- Factor out the common factor: Factor out 4X from both terms:
4X(2X – 3)
Therefore, the factored form of 8X^2 – 12X is 4X(2X – 3).
Verification of Factored Form
We can verify the factored form of 8X^2 – 12X by expanding the factored expression and simplifying it to check if it is equivalent to the original expression. Let’s multiply out the factored form 4X(2X – 3) to confirm our result:
4X(2X – 3) = 4X * 2X – 4X * 3
Expanding the terms:
8X^2 – 12X
Our result matches the original expression 8X^2 – 12X, confirming that the factored form 4X(2X – 3) is correct.
Applications of Factoring
Factoring is a fundamental algebraic concept that has various applications in mathematics and real-world scenarios. Some of the common applications of factoring include:
- Simplifying Algebraic Expressions: Factoring helps simplify complex algebraic expressions by breaking them down into simpler factors.
- Solving Equations: Factoring is used to solve equations by finding roots or solutions to the expression.
- Graphing Functions: Factoring can help in graphing functions by identifying key points such as intercepts and turning points.
- Optimizing Problems: Factoring is utilized in optimization problems to maximize or minimize values of a function.
Conclusion
Factoring is a valuable algebraic skill that simplifies expressions and equations, making mathematical calculations more manageable. By understanding the process of factoring and identifying common factors, we can find the factored form of expressions like 8X^2 – 12X. Remember to practice factoring regularly to strengthen your algebraic skills and apply them to various mathematical problems.
