Write as a product using factorization:
Problem 1 :
5! + 4!
Solution :
5! + 4!
5! Can be written as 5 × 4!
= (5 × 4!) + 4!
Factoring 4!, we get
= 4! (5 + 1)
= 4! (6)
5! + 4! = 6 × 4!
Problem 2 :
11! - 10!
Solution :
11! - 10!
11! Can be written as 11 × 10!
= (11 × 10!) - 10!
Factoring 10!, we get
= 10! (11 - 1)
= 10! (10)
11! - 10! = 10 × 10!
Problem 3 :
6! + 8!
Solution :
6! + 8!
8! Can be written as 8 × 7 × 6!
= 6! + (8 × 7 × 6!)
Factoring 6!, we get
= 6! (1 + 56)
6! + 8! = 57 × 6!
Problem 4 :
12! - 10!
Solution :
12! - 10!
12! Can be written as 12 × 11 × 10!
= (12 × 11 × 10!) - 10!
Factoring 10!, we get
= 10! (12 × 11) - 1
= 10! (132 - 1)
= 10! (131)
12! - 10! = 131 × 10!
Problem 5 :
9! + 8! + 7!
Solution :
9! + 8! + 7!
9! Can be written as 9 × 8 × 7!
= (9 × 8 × 7!) + 8! + 7!
Factoring 7!, we get
= 7! (9 × 8) + 8 + 1
= 7! (72) + 8 + 1
= 7! × 81
9! + 8! + 7! = 81 × 7!
Problem 6 :
7! - 6! + 8!
Solution :
7! - 6! + 8!
8! Can be written as 8 × 7 × 6!
= 7! - 6! + (8 × 7 × 6!)
Factoring 7!, we get
= 6! (8 × 7) + 7 - 1
= 6! (56 + 6)
= 6! (62)
7! - 6! + 8! = 62 × 6!
Problem 7 :
12! - 2 ×11!
Solution :
12! - 2 ×11!
12! Can be written as 12 × 11!
= (12 × 11!) - 2 × 11!
Factoring 11!, we get
= 11! (12) - 2 × 1
= 11! (12 - 2)
= 11! (10)
12! - 2 ×11! = 10 × 11!
Problem 8 :
3 × 9! + 5 × 8!
Solution :
3 × 9! + 5 × 8!
9! Can be written as 9 × 8!
= 3 × (9 × 8!) + 5 × 8!
Factoring 7!, we get
= 8! (3 × 9) + 5(1)
= 8! (27) + 5
= 8! (32)
3 × 9! + 5 × 8! = 32 × 8!
Simplify using factorization :
Problem 1 :
(12! - 11!) / 11
Solution :
(12! - 11!) / 11
12! can be written as 12 × 11!
= [(12 × 11!) - 11!] / 11
Factoring 11!, we get
= 11! (12 - 1) / 11
= 11! (11) / 11
= 11!
Problem 2 :
(10! + 9!) / 11
Solution :
(10! + 9!) / 11
10! Can be written as 10 × 9!
= (10 × 9!) + 9! / 11
Factoring 9!, we get
= [9! (10) + 1] / 11
= 9! (11) / 11
= 9!
Problem 3 :
(10! - 8!) / 89
Solution :
(10! - 8!) / 89
10! Can be written as 10 × 9 × 8!
= (10 × 9 × 8!) - 8! / 89
Factoring 8!, we get
= 8! (10 × 9) - 1 / 89
= 8! (90) - 1 / 89
= 8! (89) / 89
= 8!
Problem 4 :
(10! - 9!) / 9!
Solution :
10! - 9! / 9!
10! Can be written as 10 × 9!
= (10 × 9!) - 9! / 9!
Factoring 9!, we get
= 9! (10 - 1) / 9!
= 9
Problem 5 :
(6! + 5! - 4!) / 4!
Solution :
(6! + 5! - 4!) / 4!
6! Can be written as 6 × 5 × 4!
= [(6 × 5 × 4!) + (5 × 4!) - 4!] / 4!
Factoring 4!, we get
= 4![(6 × 5) + 5 - 1] / 4!
= 4! (30 + 4) / 4!
= 34
Problem 6 :
(n! + (n - 1)!) / (n - 1)!
Solution :
(n! + (n - 1)!) / (n - 1)!
n! can be written as n (n - 1)!
= n (n - 1)! + (n - 1)! / (n - 1)!
Factoring (n - 1)!, we get
= (n - 1)! [(n + 1)] / (n - 1)!
= n + 1
Problem 7 :
(n! - (n - 1)! )/ n - 1
Solution :
(n! - (n - 1)!) / (n - 1)
n! can be written as n(n - 1)
= (n(n - 1)! - (n - 1)!) / (n - 1)
Factoring (n - 1)!, we get
= (n - 1)!(n - 1) / (n - 1)
= (n - 1)!
Problem 8 :
(n + 2)! + [(n + 1)! / (n + 3)]
Solution :
(n + 2)! + [(n + 1)! / (n + 3)]
(n + 2)! can be written as (n + 2) (n + 1)!
= (n + 2) (n + 1)! + (n + 1)! / (n + 3)
Then (n + 1)! In common, so will get
= (n + 1)! [(n + 2) + 1] / (n + 3)
= (n + 1)! [(n + 3)] / (n + 3)
= (n + 1)!
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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