Understanding The Factored Form Of 8X² + 12X

What Is the Factored Form of 8x2 12x from vanghopwalters.blogspot.com

Introduction

One of the fundamental concepts in algebra is factoring. Factoring is the process of breaking down a mathematical expression into its simpler components. It involves finding the common factors and simplifying them to the lowest possible terms. In this article, we will discuss the factored form of 8x² + 12x.

Understanding the Expression 8x² + 12x

Before we dive into the factored form of the expression, let us first understand what 8x² + 12x means. This expression is a quadratic polynomial, which is a polynomial of degree two. It consists of two terms, 8x² and 12x. The coefficient of x² is 8, and the coefficient of x is 12.

What is Factored Form?

The factored form of a polynomial is the product of its factors. In other words, it is the expression written in its simplest form by identifying the common factors. For example, the factored form of x² - 4 is (x - 2)(x + 2) because it can be written as the product of the factors (x - 2) and (x + 2).

Factoring 8x² + 12x

To find the factored form of 8x² + 12x, we need to identify the common factors between the two terms. Both terms have a common factor of 4x, which we can factor out. This gives us: 8x² + 12x = 4x(2x + 3) Therefore, the factored form of 8x² + 12x is 4x(2x + 3).

Checking the Factored Form

To check if our factored form is correct, we can distribute the 4x and simplify the expression. This gives us: 4x(2x + 3) = 8x² + 12x As we can see, we get back our original expression, which means that our factored form is correct.

Why is Factoring Important?

Factoring is an essential skill in algebra and is used in various applications in mathematics and science. It helps us simplify complex expressions, solve equations, and find the roots of a polynomial. It is also used in calculus to find the derivative and integral of a function.

Factoring Techniques

There are several techniques for factoring polynomials, such as the GCF (Greatest Common Factor) method, the difference of squares method, and the quadratic formula. Each method has its advantages and disadvantages, and it is essential to know when to apply them.

Conclusion

In conclusion, the factored form of 8x² + 12x is 4x(2x + 3). Factoring is an essential skill in algebra and helps us simplify complex expressions, solve equations, and find the roots of a polynomial. There are several techniques for factoring polynomials, and it is essential to know when to apply them. By mastering factoring, we can improve our problem-solving skills and excel in mathematics and science.