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

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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].
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