What are the factors in 6x+4?
The Correct Answer and Explanation is:
To factor the expression (6x + 4), we need to identify the common factor that can be factored out from both terms.
- Identify the Greatest Common Factor (GCF):
For the expression (6x + 4), we have two terms: (6x) and (4). We need to find the greatest common factor (GCF) of these terms:
- (6x) consists of (6 \times x).
- (4) is a constant term. The GCF of (6) and (4) is (2) because (2) is the largest number that divides both (6) and (4) evenly.
- Factor Out the GCF:
Once we identify the GCF, we factor it out from each term in the expression: [
6x + 4 = 2(3x) + 2(2)
] After factoring out (2), we get: [
6x + 4 = 2(3x + 2)
] - Verify the Factorization:
To ensure the factorization is correct, we can distribute (2) back into the parentheses to check if we return to the original expression: [
2(3x + 2) = 2 \cdot 3x + 2 \cdot 2 = 6x + 4
] Since distributing (2) results in the original expression, the factorization is verified. - Final Answer:
The factors of (6x + 4) are (2) and (3x + 2). Therefore, the fully factored form of the expression is: [
6x + 4 = 2(3x + 2)
]
Explanation
Factoring is the process of breaking down an expression into simpler terms that, when multiplied together, produce the original expression. In this case, (6x + 4) is a linear expression, and factoring involves finding a common factor shared by each term. The GCF of both terms in this expression is (2). By factoring out (2), we simplify the expression and make it easier to work with, especially in cases involving more complex algebraic operations.
Factoring expressions like this is an essential skill in algebra because it simplifies equations and expressions, making it easier to solve for variables, analyze functions, or perform additional algebraic manipulations. In more advanced mathematics, factoring is also useful in calculus, where it can simplify derivatives and integrals.