Question

select the correct answer.

which expression has the same gcf as (15x^2 - 21x)?

• (18x^2 - 24x)
• (15x^2 - 21)
• (12x^2 - 15x)
• (12x^2 - 18x)

Explanation:

🆕 New Concept Discovered: Greatest Common Factor of Monomials
Finding the largest shared factor of coefficients and variables.

Step 1: Find the GCF of the given expression

To find the Greatest Common Factor (GCF) of \( 15x^2 - 21x \), we look at the coefficients and the variable parts separately:

• Coefficients (15 and 21): The greatest common factor of \( 15 \) and \( 21 \) is \( 3 \).
• Variables (\( x^2 \) and \( x \)): The highest power of \( x \) that divides both terms is \( x \).

Combining these, the GCF of the given expression is:

$$ \text{GCF} = 3x $$

Step 2: Find the GCF of each option

We need to find which option also has a GCF of \( 3x \).

• Option 1: \( 18x^2 - 24x \)
• The GCF of \( 18 \) and \( 24 \) is \( 6 \).
• The GCF of \( x^2 \) and \( x \) is \( x \).
• \(\text{GCF} = 6x\)

• Option 2: \( 15x^2 - 21 \)
• The GCF of \( 15 \) and \( 21 \) is \( 3 \).
• There is no variable in the second term, so there is no \( x \) in the GCF.
• \(\text{GCF} = 3\)

• Option 3: \( 12x^2 - 15x \)
• The GCF of \( 12 \) and \( 15 \) is \( 3 \).
• The GCF of \( x^2 \) and \( x \) is \( x \).
• \(\text{GCF} = 3x\)

• Option 4: \( 12x^2 - 18x \)
• The GCF of \( 12 \) and \( 18 \) is \( 6 \).
• The GCF of \( x^2 \) and \( x \) is \( x \).
• \(\text{GCF} = 6x\)

Step 3: Identify the matching expression

Comparing the GCFs, the expression \( 12x^2 - 15x \) has the same GCF of \( 3x \) as the original expression.

Answer:

\( 12x^2 - 15x \)