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If $(x^2 - k)(x + k) = x^3 + k(x^2 - x - 5)$ and $k\neq 0$, what is the value of $k$?

 Mar 15, 2021
 #1
avatar+112953 
+1

What are the x^2 terms?    kx^2  that is no help

 

What about the x terms?   -kx     that is no help either

 

what about the constant ?      -k^2    =  -5k    So what must k be? 

 Mar 15, 2021
 #2
avatar+111 
+1

(x- k)(x + k) = x3 + k(x2 - x - 5)

x3 - kx + kx2 - k2 = x3 + k(x2 - x - 5)

x3 + k(x2 - x - k) = x3 + k(x2 - x - 5)

 

Comparing both sides, 

 k = 5

 Mar 15, 2021

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