How to factorize this in steps? (I don't want to solve for z I want the factorization steps)

1- 0.15z^{-1} - 0.1z^{-2}

Guest Apr 23, 2017

#2**+2 **

1 - 0.15z^{-1} - 0.1z^{-2}

To get rid of the denominators, I am going to multiply the expression by the fraction (100z^{2})/(100z^{2}).

This gives 100z^{2}(1 - 0.15z^{-1} - 0.1z^{-2}) / (100z^{2}).

Multiplying out: (100z^{2} + 15z- 10) / (100z^{2}).

Now, I'm going to factor out a 5 from the numerator: 5(20z^{2} + 3z - 2) / (100z^{2}).

Cancelling the 5 from both the numerator and denominator: (20z^{2} + 3z - 2) / (20z^{2}).

20z^{2} + 3z - 2 can be factored into (5z - 2)(4z + 1).

So, an answer is: (5z - 2)(4z + 1) / (20z^{2}).

geno3141
Apr 23, 2017

#3**+2 **

If you were to solve as a quadratic,---

multiply through by (z^2) ( both sides of course,but I'm assuming you're solving for right hand side = 0) left hand side becomes

(z^2) - 0.15 z - 0.1 now multiply both sides by 100, left hand side becomes

100z^2 - 15z -10 which you can now factorise as

(20z +5)(5z -2) and solve accordingly.

Guest Apr 23, 2017