Question

The value of $k$ for which $(x+2)$ is a factor of $(x+1{)}^7+(3x+k{)}^3$ is ____.

• A. $-7$
• B. $7$
• C. $-1$
• D. $-6-3^{7/3}$

Answer 1

The correct option is B $7$

If $x+2$ is a factor.

$\therefore$Putting $x=-2$, we get

$(-2+1{)}^7+(-6+k{)}^3=0\Rightarrow (k-6{)}^3=1\Rightarrow k-6=1\Rightarrow k=7$

option B is correct