Showing posts with label function. Show all posts
Showing posts with label function. Show all posts

Factorize 2x^4 - 24x^2 - 128

We have the function

2x^4 - 24x^2 - 128 
= 2 (x^4 - 12x^2 - 64)
For the sake of simplicity, assume x^2 = t.

= 2 ((x^2)^2 - 12(x^2) - 64)
= 2 (t^2 - 12t - 64)

Now, t^2 - 12t - 64 can be easily factorized be splitting the middle term.

= 2 (t^2 + 4t - 16t - 64)
= 2 (t(t + 4) - 16(t + 4))
= 2 (t + 4)(t - 16) 


Putting back x^2 = t

= 2 (x^2 + 4)(x^2 - 16)
= 2 (x^2 + 4)(x^2 -4^2)
= 2 (x^2 + 4)(x + 4)(x - 4)

Rewrite as function as x; x = x + ((x - y) / z * 100)

We have
x = ((x - y)/z * 100)

To write it as a function of x, we'll have to take x on one side and the rest on other side of the equation.

x = x + ((x - y) / z * 100)
=> 0 = (x - y)/z * 100
=> 0 = (x - y)
=> x = y

You can now write is as y = x. y is a function of x now.