Factor out the greatest common factor from the polynomial. 4x+8
The Correct Answer and Explanation is :
To factor out the greatest common factor (GCF) from the polynomial (4x + 8), we need to identify the largest factor that both terms have in common. Let’s break this down step by step:
Step 1: Identify the terms
The given polynomial is (4x + 8), which has two terms:
- The first term is (4x).
- The second term is (8).
Step 2: Find the greatest common factor (GCF)
We need to find the greatest common factor of the coefficients of the two terms and the variable factors. Let’s examine the coefficients:
- The coefficient of (4x) is 4.
- The coefficient of 8 is 8.
The factors of 4 are: (1, 2, 4).
The factors of 8 are: (1, 2, 4, 8).
The largest number that is a factor of both 4 and 8 is 4. Therefore, the GCF of the coefficients is 4.
Next, we look at the variable factors. The first term, (4x), includes (x), but the second term, 8, does not have any variable. Since there is no common variable factor, we do not include any variable in the GCF.
Thus, the greatest common factor of the entire polynomial is 4.
Step 3: Factor out the GCF
Now, we factor out the GCF, which is 4, from the expression (4x + 8).
To do this, divide each term by 4:
- (4x \div 4 = x)
- (8 \div 4 = 2)
So, factoring out 4 from (4x + 8) gives:
[
4x + 8 = 4(x + 2)
]
Final Answer:
The factored form of (4x + 8) is (4(x + 2)).
Explanation:
Factoring out the GCF from a polynomial is a technique used to simplify the expression. The goal is to rewrite the polynomial as a product of the GCF and another polynomial. In this case, we identified that the GCF of (4x) and (8) is 4, and by dividing both terms by 4, we rewrote the expression as (4(x + 2)). This simplifies the polynomial and makes it easier to work with in further mathematical operations.