Question

select the correct answer.
which expression has a greatest common factor of 3h?
a. 3 - 9h
b. 12h + 21h²
c. 18h² - 6
d. 6h² - 2h

Explanation:

Step1: Analyze Option A

Factor \(3 - 9h\). The GCF of 3 and 9h is 3. So, \(3 - 9h = 3(1 - 3h)\). The GCF is 3, not \(3h\).

Step2: Analyze Option B

Factor \(12h + 21h^{2}\). The GCF of 12h and \(21h^{2}\) is \(3h\) (since GCF of 12 and 21 is 3, and GCF of \(h\) and \(h^{2}\) is \(h\)). So, \(12h + 21h^{2}=3h(4 + 7h)\). The GCF is \(3h\).

Step3: Analyze Option C

Factor \(18h^{2}-6\). The GCF of \(18h^{2}\) and 6 is 6. So, \(18h^{2}-6 = 6(3h^{2}-1)\). The GCF is 6, not \(3h\).

Step4: Analyze Option D

Factor \(6h^{2}-2h\). The GCF of \(6h^{2}\) and \(2h\) is \(2h\). So, \(6h^{2}-2h = 2h(3h - 1)\). The GCF is \(2h\), not \(3h\).

Answer:

B. \(12h + 21h^{2}\)