Question

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

• A. k = 0
• B. k = 5
• C. k = 7
• D. k = 10

Answer 1

The correct option is C k = 7

Let $f\left(x\right)=(x+1{)}^7+(3x+k{)}^3$
$\therefore$ $(x+2)$ is a factor of $f\left(x\right)$.
By factor theorem,
$f(-2)=0$
$\Rightarrow (-2+1{)}^7+(3(-2)+k{)}^3=0$
$\Rightarrow (-1{)}^7+(-6+k{)}^3=0$
$\Rightarrow \sqrt[3]{3(-6+k{)}^3}\Rightarrow -6+k=1$
$\therefore k=7$

So, the correct answer is option (c).