Final answer:
The greatest common factor (GCF) of 35u², 70u, and 7u³ is 7u, as 7 is the largest number that divides all coefficients and u to the power of 1 is the highest power of u present in all terms.
Step-by-step explanation:
The question asks for the greatest common factor (GCF) of the algebraic expressions 35u2, 70u, and 7u3. To find the GCF, look for the highest power of u that is present in all terms and the largest number that divides all the coefficients.
- The coefficients are 35, 70, and 7. The GCF of these numbers is 7, as it is the largest number that divides all of them.
- The highest power of u common to all terms is u1 because that is the lowest exponent of u in the given terms.
Therefore, the GCF is 7u.