Answer:
2730
Step-by-step explanation:
We want to determine the greatest common divisor of the elements of the set 
We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.
Now, 
if p-1 divides 12.
Since the of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.
Therefore, the gcd of the elements in 
and 
2*3*5*7*13=2730
Therefore, the gcd of the elements in set S is 2730.
We are given two numbers $24 and $30.
We need to find the largest three-digit number that is a multiple of both $24 and $30.
So, we need to find the largest common multiple of 24 and 30.
<em>In order to find the largest common multiple, we need to multiply both numbers.</em>
If we multiply 24 and 30, we would get
24 × 30 = 720.
Therefore, the largest three-digit number that is a multiple of both $24 and $30 is 720.
In the slope intercept form equation of a line (y=ax+b) a represents the slope, and b represents the intercept, which is -5. Thus, we know y=ax-5. The slope can be found by creating a fraction with the change in y value on top, and the change of x value on the bottom. If we have two points (4, 1) and (0, -5) we can put this into a fraction -
, which simplifies down to -6/-4, or 3/2. Thus the answer is f(x)=
x-5<span />
Use the rational roots test. The possible roots are: plus/minus 6,3,2,1
Use synthetic division and you will see that 3 is a root:
3 | 1 -3 -3 11 -6
| 3 0 -9 6
____________
1 0 -3 2 0
Use rational root again, to see that possible roots are: plus/minus 2,1
Try 2:
2 | 1 0 -3 -2
| 2 4 2
_____________
1 2 1 0
The above is x^2+2x+1 which is a perfect square: (x+1)^2
So we have the final factorization: (x-3)(x-2)(x+1)^2
So the roots are: 3, 2, -1
Where -1 is a double zero.
