Factorize 8! — 5(7!)
A. 4! 7!
B. 3 — 7!
C. 4 x 7!
D. 3! x 7!
8! - 5(7!) can be factorized as follows:
8! - 5(7!) = (8)(7!) - 5(7!)
Now, both terms have a common factor of 7!, so we can factorize it out:
(8)(7!) - 5(7!) = (8 - 5)(7!) = 3(7!)
So the factorization of 8! - 5(7!) is 3(7!), which is equivalent to option D.
To factorize 8! - 5(7!), we can simplify first by evaluating the factorials.
We know that 8! means 8 factorial, which is calculated by multiplying all the positive integers from 1 to 8: 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
Similarly, we can find the value of 7! by multiplying all the positive integers from 1 to 7: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040.
Now we can substitute these values into the expression: 8! - 5(7!) = 40,320 - 5(5,040).
Next, we can perform the multiplication: 5(5,040) = 25,200.
Finally, we can simplify the expression: 40,320 - 25,200 = 15,120.
Therefore, the factorization of 8! - 5(7!) is D. 3! x 7!.