Q. Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.9k3−6k2
Identify Numerical Coefficients and Powers: To find the greatest common factor (GCF) of 9k3 and 6k2, we need to look at the numerical coefficients and the powers of k. The numerical coefficients are 9 and 6. The GCF of 9 and 6 is 3 because both numbers are divisible by 3. For the variable part, since both terms have at least k2, the GCF will include k2.
Express Terms as Product: Now we express each term as a product of the GCF and the remaining factors. For 9k3, we can write it as 3k2×3k because 9k3 divided by 3k2 is 3k. For 6k2, we can write it as 3k2×2 because 6k2 divided by 3k2 is 2.
Factor Out the GCF: We can now factor out the GCF from the polynomial. The original polynomial is 9k3−6k2. Factoring out the GCF of 3k2, we get 3k2(3k−2).