First let's find the GCF of 27, 36, and 72:
-->Find the factors of each number:
27: 1, 3, 9, 27
36: 1, 2, 3, 4, 9, 12, 18, 36
72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
-->Now look for the factors they have in common.
1, 3, and 9
-->Now see which one is the biggest number in value
9
--> So therefore, 9 is the GCF
Now let's find the LCM of 7, 4, 10, and 12
-->Start listing all the multiples of of each number
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40... 420
7: 7, 14, 21, 28, 35, 42, 49, 56, 64, 70... 420
10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120... 420
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120... 420
(sorry got bored of typing so I fast forwarded at the '...'s)
--> The least number in value that they have in common is the LCM of those numbers
The LCM is 420
*Just saying that took forever to do that LCM part but not way too long thank goodness :p
9514 1404 393
Answer:
-3840t^4
Step-by-step explanation:
The k-th term, counting from k=0, is ...
C(5, k)·(4t)^(5-k)·(-3)^k
Here, we want k=1, so the term is ...
C(5, 1)·(4t)^4·(-3)^1 = 5·256t^4·(-3) = -3840t^4
__
The program used in the attachment likes to list polynomials with the highest-degree term last. The t^4 term is next to last.