Polynomials And Factorials Again

5x5x5-5=120

120÷2=60

60÷2=30

30÷2=15

15÷3=5

5÷5=1

1x2x3x(2x2)x5=5!

5x5x5-5 reduces to: 5(5^2-1) Factoring gives 5(6)(4) Since prime factorization of 6 is 2x3, then this becomes 2x3x4x5, which is 5!.

By BODMAS, $n!=120$ or $n=5$ .

This is a factoral method:

$\displaystyle{\begin{aligned} n! =5 \cdot 5 \cdot 5 - 5 &\Rightarrow n! = 125 - 5 \\&\Rightarrow n! = 120 \end{aligned}}$ .

You don't have to think a number for factoral to find the value of $n$ you have to find form 0 to 9 to find the equal figure.

We have to try:

For $2$ : let $n = 2$ So

$\begin{aligned}n!=120 &\Rightarrow 2!=120 \\&\Rightarrow 2 = 120 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad{ 2! =1 \cdot 2 \Rightarrow 2 } \\&\Rightarrow 2 \not = 120 \end{aligned}$

For $4$ : let $n = 2$ So

$\begin{aligned} n! =120 &\Rightarrow 4! = 120 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad{4! = 1 \cdot 2 \cdot 3 \cdot 4 \Rightarrow = 24 }\\&\Rightarrow 24 \not = 120 \end{aligned}$

For $5$ : let $n = 5$ So

$\begin{aligned} n! = 120&\Rightarrow 5! =120 \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad{5! = 1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \Rightarrow 120} \\&\Rightarrow 120 = 120 \end{aligned}$

$\therefore$ We found the value of the $n$ that makes the $120 = 5!$ . So the $n = 5$

$\large \text{FIN!!!!}$