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Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline9b26b9b^2 - 6b

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Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline9b26b9b^2 - 6b
  1. Identify Factors: We need to find the greatest common factor (GCF) of the terms 9b29b^2 and 6b6b. To do this, we will list the factors of the coefficients and the variables separately and then identify the common factors.\newlineFactors of 99: 11, 33, 99\newlineFactors of 66: 11, 22, 33, 66\newlineThe common factor for the coefficients is 33.\newlineFor the variables, since both terms have at least one '6b6b22', the common factor will include '6b6b22'.
  2. Express as Product: Now we will express each term as a product of the GCF and the remaining factors.\newlineFor 9b29b^2, we can write it as 3×3×b×b3 \times 3 \times b \times b.\newlineFor 6b6b, we can write it as 3×2×b3 \times 2 \times b.\newlineThe GCF of 9b29b^2 and 6b6b is 3b3b.
  3. Factor Out GCF: We will now factor out the GCF from each term.\newline9b29b^2 can be written as 3b×3b3b \times 3b.\newline6b6b can be written as 3b×23b \times 2.\newlineSo, the polynomial 9b26b9b^2 - 6b can be factored as:\newline9b26b=3b(3b2)9b^2 - 6b = 3b(3b - 2).