Question 1:
For this case we have that by definition, the GCF of two numbers is the largest number that is a factor of both numbers. For example, the number 10 is the biggest factor that 50 and 30 have in common.
We must find the GCF of the following expression:
[tex]30t ^ 2u + 12tu ^ 2 + 24tu[/tex]
We look for the prime factorization of each number:
[tex]30: 2 * 3 * 5\\12: 2 * 2 * 3\\24: 2 * 2 * 2 * 3[/tex]
The GCF of the three numbers is [tex]2 * 3 = 6[/tex]
So:
[tex]6tu (5t + 2u + 4)[/tex]
Answer:
Option C
Question 2:
For this case we have that by definition of power properties of the same base, that:
[tex]a ^ n * a ^ m = a ^ {n + m}[/tex]
That is, for multiplication of powers of the same base, the same base is placed and the exponents are added.
So:
[tex]b ^ n * b ^ m = b ^ {n + m}[/tex]
ANswer:
[tex]b ^ {n + m}[/tex]
Option A
