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Algebra 2 help: functions

 
Guest Oct 12, 2017
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Leading coefficient 2, zeroes   =  2, √2, -√2

 

So...we can write this as

 

2 ( x - 2) (x - √2) (x + √2)  =

2(x - 2) (x^2  - 2)  =

2 (x^3 - 2x^2 - 2x + 4)  =

2x^3 - 4x^2 - 4x + 8

 

Similarly....we have

 

Leading coefficient -1, zeroes   =  1, 1 +√3,  1-√3

 

-1 ( x -1) ( x - [1 +√3] ) ( x  - [ 1 -√3] )  =

-1 (x - 1) ( x^2  - [ 1 + √3]x  - [ 1 -√3] x  +  [1 +√3] [1 -√3] )  =

-1 (x - 1) (x^2 - x - √3x  - x + √3x  + 1  - 3 )  =

-1 (x - 1)  (x^2 - 2x -2)  =

-1( x^3 -x^2 - 2x^2 + 2x - 2x + 2) =

-1 (x^3 - 3x^2 + 2) =

-x^3 + 3x^2 - 2

 

 

cool cool cool

 
CPhill  Oct 12, 2017

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