Question
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Yen feeds his puppy the same amount of food each day. He plan to increase this amount by \( x \) oz. The expression \( 3 x+18 \) represer the total weight of food, in ounces, Yen needs for his puppy for the next three days. a. Rewrite the expression as a product of two factors. Show your work.

Ask by Carter Edwards. in the United States
Mar 20,2025

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Answer

The expression \( 3x + 18 \) can be rewritten as \( 3(x + 6) \).

Solution

To rewrite the expression \( 3x + 18 \) as a product of two factors, we can factor out the greatest common factor (GCF) from the terms in the expression. 1. **Identify the GCF**: The terms in the expression are \( 3x \) and \( 18 \). The GCF of these two terms is \( 3 \). 2. **Factor out the GCF**: We can factor \( 3 \) out of the expression: \[ 3x + 18 = 3(x + 6) \] Thus, the expression \( 3x + 18 \) can be rewritten as a product of two factors: \[ 3(x + 6) \] This shows that the total weight of food Yen needs for his puppy for the next three days can be expressed as \( 3 \) times the amount of food he plans to feed his puppy each day plus \( 6 \) ounces.

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Beyond the Answer

To rewrite the expression \( 3x + 18 \) as a product of two factors, we can factor out the greatest common factor, which is 3. Here’s how it looks: 1. Identify the common factor: Both terms \( 3x \) and \( 18 \) can be divided by 3. 2. Factor out 3: \[ 3x + 18 = 3(x + 6) \] Thus, the expression \( 3x + 18 \) can be rewritten as \( 3(x + 6) \). If you need to find more ways to approach this kind of problem, remember that factoring is all about finding common elements. One common mistake is to overlook the greatest common factor, so always check if there's something you can factor out first! Keep practicing with different expressions, and you'll become a factoring whiz in no time!

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