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Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial. \newline6n39n26n^3 - 9n^2

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Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial. \newline6n39n26n^3 - 9n^2
  1. Find GCF of Terms: We need to find the greatest common factor (GCF) of the terms 6n36n^3 and 9n29n^2. To do this, we will list the factors of the coefficients (66 and 99) and the common powers of nn.
  2. List Factors: The factors of 66 are 11, 22, 33, and 66. The factors of 99 are 11, 33, and 99. The common factors of 66 and 99 are 11 and 33. Since we are looking for the greatest common factor, we choose 33.
  3. Identify Common Factors: Both terms have a power of nn, so we also look at the lowest power of nn that is common to both terms. The lowest power of nn common to both terms is n2n^2.
  4. Determine GCF: Combining the common numerical factor and the common variable factor, we get the GCF of 6n36n^3 and 9n29n^2 as 3n23n^2.
  5. Divide by GCF: Now we divide each term by the GCF to factor it out. For the first term, 6n36n^3 divided by 3n23n^2 is 2n2n. For the second term, 9n29n^2 divided by 3n23n^2 is 33.
  6. Write Factored Polynomial: Writing the original polynomial with the GCF factored out, we get 3n2(2n3)3n^2(2n - 3).