Question

If $(x+k)$ is a factor of the polynomial $x^2-2x-15$ and $x^3+a$. Find k and a.

• A. $k=3$ and $a=27$
• B. $k=-5$ and $a=-125$
• C. both $A$ and $B$
• D. none

Answer 1

Answer: (C)

both $A$ and $B$

$(x+k)$ is factor $x^2-2x-15$ and $x^3+a$

$\therefore k(2+k)-15=0$

$\Rightarrow k^2+2k-15=0$

$\Rightarrow k^2+5k-3k-15=0$

$\Rightarrow k(k+5)-3(k+5)=0$

$\Rightarrow k=3$ or $-5$

$\therefore$ the solution sets for $(k,a)$ are

$(3,27)$ and $(-5,-125)$