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Given:

 Feb 28, 2019
 #1
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+2

The only hard part is the second part

 

f(x) =   x - 3

 

g(x) + f(x)  =    ( 2x^2 + 5x - 1)  + ( x - 3)   =   2x^2 + 6x - 4

 

So   [ g(x) + f(x) ]^2 = 

 

 [ 2x^2 + 6x - 4]^2   = 

 

[ 2 (x^2 + 3x - 2] ^2  =  

 

4 [  x^2 + 3x  - 2 ]  [x^2 + 3x - 2 ]  =

 

4      [  (x^4 + 3x^3 - 2x^2) + ( 3x^3 + 9x^2 - 6x ) -2x^2 - 6x + 4 ] =

 

4 [ x^4   + 6x^3  + 5x^2 - 12x + 4 ]  =

 

4x^4 + 24x^3  + 20x^2 - 48x + 16

 

So

 

f(x)  - [ g(x) + f(x) } ^ 2 =

 

(x - 3) - [ 4x^4 + 24x^3 + 20x^2 - 48x + 16 ] =

 

-4x^4 - 24x^3 - 20x^2 + 49x - 19

 

 

cool coolcool

 Mar 2, 2019

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