If X-2 Is A Factor Of X^3-kx^2+kx+2, Where K Is A Constant, What Is The ...

If #x-2# is a factor of #x^3-kx^2+kx+2#, where #k# is a constant, what is the value of #k#? Precalculus

1 Answer

sjc Jun 4, 2017

#k=5#

Explanation:

use the factor theorem which states that

for a polynomial #P(x);# #" "[(x-a) " is a factor]"=>P(a)=0#

so

#P(x)=x^3-kx^2+kx+2#

#because (x-2) " is a factor"#

#P(2)=2^3-kxx2^2+2k+2=0#

#=>8-4k+2k+2=0#

#10=2k#

#:.k=5#

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