Q. Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial.6y3+9y
Identify GCF: We need to find the greatest common factor (GCF) of the terms 6y3 and 9y. To do this, we look for the highest power of y that is in both terms and the largest number that divides both 6 and 9.
Determine Highest Power: The highest power of y that is common to both terms is y, since the second term does not have a power higher than 1. The largest number that divides both 6 and 9 is 3. Therefore, the GCF is 3y.
Divide by GCF: Now we divide each term by the GCF to find the remaining factors. For the first term, 6y3 divided by 3y gives us 2y2. For the second term, 9y divided by 3y gives us 3.
Write Factored Form: We can now write the original polynomial as the product of the GCF and the remaining factors. The factored form of 6y3+9y is 3y(2y2+3).