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Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline9v3+6v29v^3 + 6v^2

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Q. Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline9v3+6v29v^3 + 6v^2
  1. Identify Numerical Coefficients: To find the greatest common factor (GCF) of 9v39v^3 and 6v26v^2, we need to look at the numerical coefficients and the variable parts separately. The numerical coefficients are 99 and 66. The common factors of 99 and 66 are 11 and 33. Since 33 is the greatest common numerical factor, we will use that. For the variable part, both terms have at least v2v^2, so we can factor out v2v^2 as well.
  2. Find Common Factors: Now we will express each term as a product of the GCF and the remaining factors. For the first term, 9v39v^3, we divide it by the GCF, which is 3v23v^2, to find the remaining factor. 9v39v^3 divided by 3v23v^2 is 3v3v. So, the first term can be written as 3v2×3v3v^2 \times 3v.
  3. Express Terms as Products: For the second term, 6v26v^2, we also divide it by the GCF, which is 3v23v^2, to find the remaining factor. 6v26v^2 divided by 3v23v^2 is 22. So, the second term can be written as 3v2×23v^2 \times 2.
  4. Write Original Polynomial: Now we can write the original polynomial, 9v3+6v29v^3 + 6v^2, as a product of the GCF and the sum of the remaining factors. This gives us 3v23v+3v223v^2 * 3v + 3v^2 * 2, which simplifies to 3v2(3v+2)3v^2(3v + 2).