The expression 8x+2 factored using the gcf is a fundamental concept in algebra that involves identifying the greatest common factor (GCF) of the terms in the expression and then factoring it out. This process simplifies algebraic expressions, making them easier to solve and understand.
To factor 8x+2 using the GCF, we first identify the GCF of 8x and 2, which is 2. We then factor out the GCF from each term in the expression, resulting in 2(4x+1). This simplified expression is easier to work with and can be used in various applications, such as solving equations and simplifying complex expressions.
The Expression 8x+2 Factored Using the GCF
In mathematics, factoring is a technique used to simplify algebraic expressions by expressing them as a product of simpler factors. One common method of factoring is to identify and extract the greatest common factor (GCF) of the terms in the expression.
1. GCF of 8x+2, The expression 8x+2 factored using the gcf is
The GCF of two or more algebraic terms is the greatest factor that divides each term without leaving a remainder. To find the GCF of 8x and 2, we first identify their prime factors:
- 8x = 2 3– x
- 2 = 2 1
The GCF of 8x and 2 is the product of the common prime factors raised to their lowest exponents, which is 2 1= 2.
2. Factoring Using GCF
To factor 8x+2 using the GCF, we divide each term by the GCF, which is 2:
- (8x) / 2 = 4x
- (2) / 2 = 1
The factored expression is therefore:
8x+2 = 2(4x+1)
3. Simplified Expression
The expression 8x+2 has been simplified by factoring out the GCF of 2. The simplified expression, 2(4x+1), is equivalent to the original expression, but it is in a more factored form.
Simplifying expressions using GCF makes them easier to work with and solve. For example, the simplified expression 2(4x+1) can be easily solved for x by dividing both sides by 2.
4. Applications of Factoring
Factoring algebraic expressions has many real-world applications, including:
- Solving equations
- Simplifying complex expressions
- Finding the zeros of a polynomial
- Solving optimization problems
For example, factoring 8x+2 using GCF would be useful in solving the equation 8x+2=0. By factoring out the GCF, we can easily see that the solution to the equation is x=-1/4.
Q&A: The Expression 8x+2 Factored Using The Gcf Is
What is the GCF of 8x+2?
The GCF of 8x+2 is 2.
How do you factor 8x+2 using the GCF?
To factor 8x+2 using the GCF, we first identify the GCF of 8x and 2, which is 2. We then factor out the GCF from each term in the expression, resulting in 2(4x+1).
What are the benefits of factoring algebraic expressions using the GCF?
Factoring algebraic expressions using the GCF simplifies the expressions, making them easier to solve and manipulate. It also helps in identifying common factors and patterns within the expression.
