+0  
 
0
100
5
avatar

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

 

 

thx!

 Aug 22, 2020
 #1
avatar
0

Since f(x) is divisible by x^3, f(x) is of the form ax^5 + bx^4 + cx^3.

 

You then want ax^5 + bx^4 + cx^3 + 2 to be divisible by (x + 1)^3.  Using long division, you get the equations

-10a  + 6b - 3c = 0

4a - 3b + 2c = 0

-a + b - c + 2 = 0

==> a = 6, b = 16, c = 12

 

So f(x) = 6x^5 + 16x^4 + 12x^3.

 Aug 22, 2020
 #2
avatar+111597 
0

I do not think that this is possible.

Are you sure your question is copied properly?

 Aug 23, 2020
 #3
avatar+1038 
+2

I'm pretty sure that the question is copied properly, as I have seen it before....but yes, I agree that this one is a bit tricky! Congrats guest for solving it!

 

:)

ilorty  Aug 23, 2020
 #4
avatar+31320 
+1

See https://web2.0calc.com/questions/please-help-asap-polynomial-division

 Aug 23, 2020
 #5
avatar+111597 
+1

Thanks Alan and ilorty     laugh   

Melody  Aug 24, 2020

36 Online Users