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If $p(x) = x^4 - 3x + 2$, then find the coefficient of the $x^3$ term in the polynomial $(p(x))^3$.

 Aug 1, 2018
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If $p(x) = x^4 - 3x + 2$, then find the coefficient of the $x^3$ term in the polynomial $(p(x))^3$.

 

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

 

x^8 - 3x^5 + 2x^4

                  -3x^4  + 9x^2 - 6x

                 +2x^4              -6x    + 4

_____________________________

x^8  - 3x^5  + x^4  + 9x^2 - 12x  + 4

 

And

 

[p(x)]^2  * [p(x) ] =  [p(x)] ^3  =

 

 [x^8  - 3x^5  + x^4  + 9x^2 - 12x  + 4]  * [ x^4 - 3x + 2 ]

 

The x^3  term  will be    9x^2 * -3x   =   - 27x^3

 

So.....the coefficient is   -27

 

 

cool cool cool

 Aug 1, 2018

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