Question

$\Delta =\left|\begin{array}{ccc}a& a^2& 0\\ 1& 2a+b& (a+b)\\ 0& 1& 2a+3b\end{array}\right|$ is divisible by

• A. $a+b$
• B. $a+2b$
• C. $2a+3b$
• D. $a^2$

Answer 1

The correct option is A $a+b$

Expanding by $R_3$,
$=-1\left(a\right(a+b\left)\right)+(2a+3b)(2a^2+ab-a^2)$
$=-1\left(a\right(a+b\left)\right)+(2a+3b)a(a+b)$
$=a(a+b)(2a+3b-1)$