Factor 2X<Sup>2</Sup> 5X<Sup>3</Sup>

How to Solve 2x^2 + 5x 3 = 0 by Factoring YouTube from www.youtube.com

Introduction

Factoring is an important skill in algebra that involves breaking down a polynomial expression into simpler terms. In this article, we will discuss the process of factoring the expression 2x² 5x³ and provide step-by-step instructions on how to do it.

Step 1: Identify the Common Factor

The first step in factoring 2x² 5x³ is to identify the common factor. In this case, the common factor is x². To see why, we can rewrite the expression as 2x² (5x).

Step 2: Rewrite the Expression

Now that we have identified the common factor, we can rewrite the expression as follows: 2x² (5x) = 2x² (x * 5x²) This step involves breaking down the remaining factors into their prime factors. In this case, we have broken down 5x³ into x and 5x².

Step 3: Combine Like Terms

The final step in factoring 2x² 5x³ is to combine like terms. We can do this by adding the exponents of x, which gives us: 2x² (x * 5x²) = 2x³ * 5x²

Final Answer

Therefore, the fully factored form of 2x² 5x³ is: 2x² 5x³ = 2x³ * 5x²

Conclusion

Factoring expressions like 2x² 5x³ can be challenging, but by following these simple steps, we can easily break down the expression into simpler terms. Remember to always look for the common factor, rewrite the expression, and combine like terms to get the fully factored form. With practice, factoring will become second nature, and you will be able to factor more complex expressions with ease.

Tips and Tricks

- Always look for the common factor first, as this can make factoring much easier. - If you're having trouble breaking down the remaining factors, try using a factor tree to help you identify the prime factors. - Practice makes perfect! The more you practice factoring, the more comfortable you will become with the process.

Example Problems

1. Factor 3x² 6x. Solution: The common factor is 3x, so we can rewrite the expression as 3x (x * 2) and combine like terms to get 6x². Therefore, the fully factored form is 3x * 2 * x = 6x². 2. Factor 4x³ 12x². Solution: The common factor is 4x², so we can rewrite the expression as 4x² (x * 3) and combine like terms to get 12x³. Therefore, the fully factored form is 4x² * 3 * x = 12x³.