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Which of the following terms have a GCF of 6p^(3) ? Select two options. i. 12p^(3)r 27p^(4)q ii. 45p^(3)q^(6) iii. 54p^(3) iv. 63p^(3)q^(6)

User Beryl
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The correct options are iii. 54p^(3) and iv. 63p^(3)q^(6

To determine which terms have a greatest common factor (GCF) of 6p^(3), we need to look for factors that are common to all the terms.

First, let's break down the terms into their prime factors:

i. 12p^(3)r = 2 * 2 * 3 * p * p * p * r
ii. 27p^(4)q = 3 * 3 * 3 * p * p * p * p * q
iii. 54p^(3) = 2 * 3 * 3 * 3 * p * p * p
iv. 63p^(3)q^(6) = 3 * 3 * 7 * p * p * p * q * q * q * q * q * q

Now, let's identify the common factors among the terms:

i. 12p^(3)r = 2 * 2 * 3 * p * p * p * r
ii. 27p^(4)q = 3 * 3 * 3 * p * p * p * p * q
iii. 54p^(3) = 2 * 3 * 3 * 3 * p * p * p
iv. 63p^(3)q^(6) = 3 * 3 * 7 * p * p * p * q * q * q * q * q * q

From the prime factorization, we can see that the common factors are 2, 3, and p^(3).

Among the given options, only iii. 54p^(3) and iv. 63p^(3)q^(6) have a GCF of 6p^(3). The other options either don't have a factor of 6 or don't have a factor of p^(3).

User Nilesh Panchal
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