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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 22, 2017
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 #1
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1- 0.15z-1 - 0.1z-2

Guest Apr 23, 2017
 #2
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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
 #3
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\(1- 0.15z-1 - 0.1z-2\\ =1-1-2  - 0.15z - 0.1z\\ =   -2  - 0.25z \\ = -0.25(8+z) \)

 

or

 

\(1- 0.15z^{-1} - 0.1z^{-2}\\ 1- \frac{0.15}{z} -\frac{ 0.1}{z^2}\\ \frac{1}{100z^2}(100z^2- 15z -10)\\\)

 

sqrt(15^2+4*100*10) = 65

(15+65)/200 = 0.4

(15-65)/200 = -0.25

 

\(=\frac{1}{100z^2}(z-0.4)(z+0.25)\\ =\frac{1}{100z^2}(z-0.4)(z+0.25)\\\)

Melody  Apr 23, 2017
edited by Melody  Apr 23, 2017

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