Q. Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial. 2f3+4f2
Find GCF and Common Power: We need to find the greatest common factor (GCF) of the terms 2f3 and 4f2. To do this, we look for the highest power of f that is common to both terms and the largest number that divides both coefficients.The coefficients are 2 and 4, and the GCF of these numbers is 2.Both terms have at least an f2 in them, so we can factor out f2 as well.Therefore, the GCF of 2f3 and 4f2 is 4f20.
Factor Out GCF: Now we will express each term as a product of the GCF and the remaining factors.For the first term, 2f3, we divide it by the GCF, 2f2, to get the remaining factor:2f3÷2f2=f.For the second term, 4f2, we divide it by the GCF, 2f2, to get the remaining factor:4f2÷2f2=2.
Express Terms as Product: We can now write the original polynomial as a product of the GCF and the sum of the remaining factors: 2f3+4f2=2f2(f+2).This is the factored form of the polynomial using the greatest common factor.