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When the expression (2x^4+3x^3+x-14)(3x^{10}-9x^7+9x^4+30)-(x^2+5)^8 is expanded, what is the degree of the resulting polynomial?

 Apr 9, 2021
 #1
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 (2x^4+3x^3+x-14)(3x^{10}-9x^7+9x^4+30)-(x^2+5)^8

 

We  only  need  to see  that  the  highest  degree  polynomial  resulting  from the  multiplication  of  the  first two polynomials  is    2x^4  *  3x^10  =  6x^14  =    14 th  degree

 

The  highest  degree  of  the  last poltnomial  is  - (x^2)^8  =  -x^16  =    16

 

So....the  degree  of the resulting polynomial  is  16

 

 

cool cool cool

 Apr 9, 2021

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