How do you determine the GCF of the polynomial terms 33x^3 and 18x^6?

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To find the GCF (Greatest Common Factor) of the polynomial terms 33x3 and 18x6, we will follow these steps:

  1. Identify the coefficients of the terms. The coefficients are the numerical parts, which are 33 and 18.
  2. Find the GCF of the numerical coefficients:
    • The factors of 33 are 1, 3, 11, and 33.
    • The factors of 18 are 1, 2, 3, 6, 9, and 18.
    • The common factors of 33 and 18 are 1 and 3.
    • Therefore, the GCF of 33 and 18 is 3.
  3. Next, identify the variables and their exponents in each term. The first term has x3, and the second term has x6. To find the GCF of the variables, take the variable with the lowest exponent.
  4. The GCF of x3 and x6 is x3.
  5. Finally, combine the GCF of the coefficients and the GCF of the variables:
    • The overall GCF is 3x3.

In conclusion, the GCF of the polynomial terms 33x3 and 18x6 is 3x3.

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