If the expression $$px^3 - qx^2 - 7x - 6$$ is completely divisible by $$x^2 - x - 6$$, then what is the value of p and q respectively?

Expression : $$f(x)px^3 - qx^2 - 7x - 6$$ is divisible by $$x^2 - x - 6$$

=> $$x^2-x-6=0$$

=> $$(x-3)(x+2)=0$$

=> $$x=3,-2$$

Thus, $$f(3)=0$$

=> $$p(3)^3-q(3)^2-7(3)-6=0$$

=> $$27p-9q-21-6=0$$

=> $$27p-9q=27$$

=> $$3p-q=3$$ -----------(i)

Also, $$f(-2)=0$$

=> $$p(-2)^3-q(-2)^2-7(-2)-6=0$$

=> $$-8p-4q+14-6=0$$

=> $$8p+4q=8$$

=> $$2p+q=2$$ -----------(ii)

Adding equations (i) and (ii),

=> $$5p=3+2=5$$

=> $$p=1$$

Substituting it in equation (ii), => $$q=2-2(1)=0$$

=> Ans - (B)