To factor the expression 14w^11 + 35w^7, you can first find the greatest common factor (GCF) of the two terms and then factor it out. In this case, the GCF is 7w^7 because it's the largest term that can be factored out of both terms:
14w^11 + 35w^7 = 7w^7(2w^4 + 5)
So, the factored form of 14w^11 + 35w^7 is 7w^7(2w^4 + 5).