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+2
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avatar+79 

 

 

 

 

 

 

 

 

Find a polynomial f(x) of degree 5 such that both of these properties hold:

 f(x) is divisible by x^3

 f(x)+2 is divisible by (x+1)^3

 

\(Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet$ $f(x)+2$ is divisible by $(x+1)^3$\)

 Mar 13, 2021
 #1
avatar+311 
0

I believe this question is one heureka already solved, the link is

https://web2.0calc.com/questions/find-a-polynomial-f-x-of-degree-5-such-that-both

 

Yay!

 Mar 13, 2021
 #2
avatar+79 
+1

no that one is -1 but this one +2 very similar 

Dennis070sinneD  Mar 13, 2021
 #3
avatar+311 
+2

f(x)+2=ax^+bx^4+cx^3+2=(x^3+3x^2+3x+1)(dx^2+ex+f) (my head hurts)

 

If you multiply it out, you get these "variables"

 

a=d, b=e+3d, c=f+3e+3d, d+3e+3f=0, e+3f=0, f=2

 

Solve for abcdef

 

f(x)=ax^5+bx^4+cx^3

 

Yay!

 Mar 13, 2021
 #4
avatar+79 
+1

thanks for the help 

 Mar 13, 2021

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