Question #10308

by factor theorem determine the value of k for which x+2 is a factory of (x+1)^7 + (2x+k)^3

Expert's answer

If x+2 is factor of given polynomial then x=-2 is a root of equation (x+1)^7 +

(2x+k)^3=0.

So (-2+1)^7+(k-4)^3=0

(k-4)^3=1

k-4=1

k=5

(2x+k)^3=0.

So (-2+1)^7+(k-4)^3=0

(k-4)^3=1

k-4=1

k=5

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