Question

If $x^2-x-6$ and $x^2+3x-18$ have a common factor (x - a) then find the value of a.

Answer 1

$x^2-x-6=x^2-3x+2x-6$

$=x(x-3)+2(x-3)$

$=(x+2)(x-3)$ .......$\left(1\right)$

$x^2+3x-18=x^2+6x-3x-18$

$=x(x+6)-3(x+6)$

$=(x+6)(x-3)$ ........$\left(2\right)$

Comparing $\left(1\right)$ and $\left(2\right)$ the common factor is $(x-3)$ where $a=3$

$\therefore a=3$