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

i dont want the answer can i just have a hint?

 Nov 26, 2020
 #1
avatar+116126 
+1

(x + 1)^3  =   x^3  + 3x^2  +3x  +  1

 

For our polynomial to have a degree less than 2, we  need  to cancel  the  x^3  and 3x^2  terms

 

So     q (x)   will  do this  if  it is   something like  (-x -3)

 

Note  that

 

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

 

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

 

3x +  1      and this  is a degree < 2

 

(note  that other answers are possible ....but this answer for q(x)  seems the easiest )

 

 

cool cool cool

 Nov 26, 2020
 #2
avatar+110 
+1

Yep, this one works! In general, you want to be canceling out the \(x^3,x^2\) in order to get a polynomial with degree less than 2. Do you understand why? (note: I'm talking to the original poster)

OlympusHero  Nov 26, 2020
edited by OlympusHero  Nov 26, 2020

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