Q. Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial. 4r3−6r
Identify GCF: We need to find the greatest common factor (GCF) of the terms 4r3 and 6r. To do this, we look for the highest power of r that is in both terms and the largest number that divides both 4 and 6. The highest power of r common to both terms is r (since the second term is only to the first power). The largest number that divides both 4 and 6 is 2. Therefore, the GCF is 6r0.
Divide by GCF: Now we divide each term by the GCF to find the remaining factors.For the first term, 4r3 divided by 2r gives us 2r2.For the second term, 6r divided by 2r 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 the polynomial is 2r(2r2−3).