Question

find the value of k for which (x+2) is a factor of (x+1)^7+(3x+k)^3

Answer 1

Answer:

Value of k = 7

Step-by-step explanation:

$Let\: p(x) = (x+1)^{7}+(3x+k)^{3}$

/* If (x+2) is a factor of p(x) then p(-2)=0

$(-2+1)^{7}+[3(-2)+k]^{3}=0$

$\implies (-1)^{7}+(-6+k)^{3}=0$

$\implies -1 + (-6+k)^{3}=0$

$\implies (-6+k)^{3}=1$

$\implies -6+k = 1$

$\implies k = 1+6= 7$

Therefore,

Value of k = 7

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