Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Join our Q&A platform to connect with experts dedicated to providing precise answers to your questions in different areas. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Factor the expression [tex]\(4x + 32\)[/tex]. Explain each step you take in the process.

Sagot :

GinnyAnswer
To factor the given expression [tex]\( 4x + 32 \)[/tex], follow these steps:

### Step 1: Identify the Greatest Common Factor (GCF)
First, we need to find the greatest common factor (GCF) of the terms in the expression. The terms are [tex]\( 4x \)[/tex] and [tex]\( 32 \)[/tex].

- The coefficient of [tex]\( 4x \)[/tex] is [tex]\( 4 \)[/tex].
- The constant term is [tex]\( 32 \)[/tex].

To find the GCF of 4 and 32, note that 32 is divisible by 4, and the largest number that divides both 4 and 32 without leaving a remainder is 4. Therefore, the GCF of [tex]\( 4x \)[/tex] and [tex]\( 32 \)[/tex] is [tex]\( 4 \)[/tex].

### Step 2: Factor Out the GCF
Next, we factor the GCF out of each term in the expression:

1. Write the GCF [tex]\( 4 \)[/tex] outside the parentheses.
2. Divide each term by the GCF and place the results inside the parentheses.
- [tex]\( 4x \div 4 = x \)[/tex]
- [tex]\( 32 \div 4 = 8 \)[/tex]

Thus, when we factor out the GCF, we get:
[tex]\[ 4x + 32 = 4(x + 8) \][/tex]

### Conclusion
The factored form of the expression [tex]\( 4x + 32 \)[/tex] is:
[tex]\[ 4(x + 8) \][/tex]

So the final expression after factoring is [tex]\( 4(x + 8) \)[/tex].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.