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