Thread: Pre-Calc Help Please!

I had a problem that states: "Determine all values of k such that x^2-kx-6 can be factored by x-2." I had no idea what the answer was and left it blank. Can you please tell me how i would go through doing a problem like that. Thank you.

Originally Posted by aussiekid90

I had a problem that states: "Determine all values of k such that x^2-kx-6 can be factored by x-2." I had no idea what the answer was and left it blank. Can you please tell me how i would go through doing a problem like that. Thank you.

Remember by the theory of polynomial is a factor of only if 2 is a zero of this polynomial, thus, , thus, thus, .

Now for the check, the polynomial is which factors into thus, it works.
Q.E.D.

Would this be the only possiblity because the problem states find all possible solutions for K

Originally Posted by aussiekid90

Would this be the only possiblity because the problem states find all possible solutions for K

Yes, look at my derivation, only one possibility.