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Find a polynomial q(x) such that (x+1)^3+x^2*q(x) has degree less than 2.

 

I don't know where to start so can someone give me a place where to solve. I don't need answers because then I can solve it by myself.

 

Thanks!

 Nov 20, 2020
 #1
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(x + 1)^3  =  x^3  + 3x^2  + 3x  + 1

 

All  we  require is that  some  q(x)  can be  found such that  the x^3  and 3x^2  terms in the first polynomial can be canceled

 

Let  q (x)   be     (-x - 3)

 

So notice that

 

x^2   * q(x)  =   x^2  (-x - 3)   =  -x^3 -3x^2

 

So

 

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

 

3x  + 1

 

And  this is a polynomial  of  less than degree 2

 

(Note that  the choice of q(x)  isn't unique.... there are many other possibilities)

 

cool cool cool

 Nov 20, 2020

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