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