Find k such that the Polynomial P(x)=-2x+kx^2+2x+4 is divisible by x-2.

Keyla Koch 2022-10-24 Answered
Find k such that the polynomial P ( x ) = 2 x 3 + k x 2 + 2 x + 4 is divisible by x-2.
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Answers (1)

Dobricap
Answered 2022-10-25 Author has 14 answers
P ( x ) = 2 x 3 + k x 2 + 2 x + 4
As ( x 1 ) is a factor of polynomial p ( x ) = 2 x 3 + k x + 2 x + 4
So p ( 2 ) = 0 2 ( 2 ) 3 + k ( 2 ) 2 + 2 ( 2 ) + 4 = 0 2 ( 8 ) + k ( 4 ) + 4 + 4 = 0 16 + 4 k + 8 = 0 8 + 4 k = 0 4 k = 8 k = 8 4 k = 2
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