How to Factor the Expression 2s^3 - 6s^2 Easily
Quick Answer
To factor the expression 2s^3 - 6s^2, identify the greatest common factor (GCF), which is 2s^2. This leads to the factored form: 2s^2(s - 3). Use Desmos to visualize the expressions.
Factoring polynomials is an essential skill in mathematics, and it helps simplify problems and make complex equations easier to solve. In this case, we will factor the polynomial expression 2s^3 - 6s^2 step by step.
### Understanding the Problem
The expression given is 2s^3 - 6s^2. Our goal is to factor it, meaning we want to rewrite the expression as a product of simpler expressions. The first step in this process is to determine the greatest common factor (GCF) of the terms in the polynomial.
### Step-by-Step Factoring Process
1. **Identify Coefficients**: The coefficients in our expression are 2 and -6. The GCF of these numbers is 2, since 2 is the largest number that divides both evenly.
2. **Identify Variables**: Now, we look at the variable parts: s^3 and s^2. The GCF for the variables is s^2, as it's the lowest power of s present in both terms.
3. **Combine the GCF**: Therefore, the overall GCF of the expression 2s^3 - 6s^2 is 2s^2.
4. **Factor Out the GCF**: Next, we factor out 2s^2 from each term in the expression:
- For the first term: 2s^3 ÷ 2s^2 = s
- For the second term: -6s^2 ÷ 2s^2 = -3
5. **Write the Factored Form**: After factoring out the GCF, we can rewrite our expression as:
**2s^2(s - 3)**
### Visualizing with Desmos
To further understand the factoring process, you can use the Desmos Scientific or Graphing Calculator. In the Desmos Scientific Calculator, you can input the original expression and the factored form separately:
- Type `2s^3 - 6s^2` to see the original polynomial.
- Then type `2s^2(s - 3)` to visualize the factored form.
In the Graphing Calculator, this will help you see that both expressions create the same curve, confirming that our factoring is correct. Graphing can be a powerful tool for visual learners and can enhance your understanding of polynomial behavior.
### Real-World Applications
Factoring is not just an academic exercise; it has real-world applications in fields such as engineering, physics, and economics, where complex equations need to be simplified. Understanding how to factor expressions can help in solving problems more efficiently and can provide insights into the relationships between different variables.
By mastering how to factor expressions like 2s^3 - 6s^2, you are building a solid foundation for more advanced math concepts. Keep practicing, and soon you will find factoring to be a straightforward task!
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