Question

For what value of k, the polynomial 2x^3-kx^2+3x+10 is divisible by (x+2)

Answer 1

P(x) = 2x^3 - kx^2 +3x +10

P(-2) = 2 (-2)^3 - k(-2)^2 +3(-2)+ 10

=> 0 = - 16 - 4k - 6 + 10

=> 0 = - 22 +10 - 4k

=> 4k = - 12

=> k = - 3

Answer 2

f(x)=2x^3-kx^2+3x+10
g(x)=x+2
zero value of g(x)=x=-2
f(-2)=2(-2)^3-k(-2)^2+3(-2)+10=0
-16-4k-6+10=10
-4k-12=10
-4k=10+12=22
k=22/-4=-5.5
therefore value of k=-5.5
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