if (x-3) is a factor of x^2-px-x, find the value of p

Question

loser66 · Answer

take long division or synthetic to get value of p, I got p = 2. How about you??

anonymous · Answer

same here. but my book says the ans is 1. I guess its wrong.

loser66 · Answer

ok, let check:
if p =1 , then the expression is $x^2 -x -x = x^2-2x$
factor x out, we have x(x-2) , so that x -3 can't be its factor --> p=1 is not the right answer.
Now, our result is p =2
then, the expression is $x^2 -2x -x = x^2 -3x$
factor x out, we get x(x-3) . It shows x-3 is one of the factor of the expression $ x^2 -px -x$ when p =2.
Proof done.