Bot GPT 4-o mini To factor the expression \( 36x + 54y + 36z + 12 \), we first look for the greatest common factor (GCF) of the coefficients.
The coefficients are:
- \( 36 \)
- \( 54 \)
- \( 36 \)
- \( 12 \)
Let's find the GCF:
- The prime factorization of \( 36 \) is \( 2^2 \times 3^2 \).
- The prime factorization of \( 54 \) is \( 2 \times 3^3 \).
- The prime factorization of \( 12 \) is \( 2^2 \times 3 \).
The GCF of \( 36, 54, 36, \) and \( 12 \) is \( 6 \) (the lowest powers of the prime factors: \( 2^1 \) and \( 3^1 \)).
Now, we will factor out \( 6 \) from the entire expression:
\[ 36x + 54y + 36z + 12 = 6(6x) + 6(9y) + 6(6z) + 6(2) \]
This can be rewritten as:
\[ = 6(6x + 9y + 6z + 2) \]
Thus, the factored form of the expression \( 36x + 54y + 36z + 12 \) is:
\[ \boxed{6(6x + 9y + 6z + 2)} \]
Here, \( 6 \) is a whole number greater than \( 1 \), fulfilling the requirement.
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