Question

select the correct answer.

which expression has a greatest common factor of \\(3h\\)?

\\(18h^2 - 6\\)
\\(12h + 21h^2\\)
\\(6h^2 - 2h\\)
\\(3 - 9h\\)

Explanation:

Analyze the first option

$$ \text{Expression: } 18h^2 - 6 $$

The terms are \(18h^2\) and \(-6\).
The greatest common numerical factor of \(18\) and \(6\) is \(6\).
Since the second term does not contain \(h\), there is no variable factor.
The GCF is \(6\).

Analyze the second option

$$ \text{Expression: } 12h + 21h^2 $$

The terms are \(12h\) and \(21h^2\).
The greatest common numerical factor of \(12\) and \(21\) is \(3\).
The greatest common variable factor of \(h\) and \(h^2\) is \(h\).
The GCF is \(3 \cdot h = 3h\).

Analyze the remaining options

$$ \text{Expression: } 6h^2 - 2h $$

The terms are \(6h^2\) and \(-2h\).
The greatest common numerical factor of \(6\) and \(2\) is \(2\).
The greatest common variable factor of \(h^2\) and \(h\) is \(h\).
The GCF is \(2h\).

$$ \text{Expression: } 3 - 9h $$

The terms are \(3\) and \(-9h\).
The greatest common numerical factor of \(3\) and \(9\) is \(3\).
Since the first term does not contain \(h\), there is no variable factor.
The GCF is \(3\).

Answer:

• (A) \(18h^2 - 6\)
• (B) \(12h + 21h^2\) (Correct answer)
• (C) \(6h^2 - 2h\)
• (D) \(3 - 9h\)