neniyurrr neniyurrr

24-01-2020
Mathematics

contestada

if k is a constant, what is the value of k such that the polynomial k^2x^3 - 6kz+9 is
divisible by x-1?

Respuesta :

LammettHash LammettHash

24-01-2020

[tex]x-1[/tex] divides [tex]p(x)=k^2x^3-6kx+9[/tex] if the remainder is [tex]p(1)=0[/tex]. (This is the remainder theorem)

Then we must have

[tex]p(1)=k^2-6k+9=(k-3)^2=0\implies\boxed{k=3}[/tex]

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