• Jan 30th 2006, 11:29 AM
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.
• Jan 30th 2006, 12:35 PM
ThePerfectHacker
Quote:

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 \$\displaystyle (x-2)\$ is a factor of \$\displaystyle f(x)=x^2-kx-6\$ only if 2 is a zero of this polynomial, thus, \$\displaystyle f(2)=0\$, thus, \$\displaystyle 4-2k-6=0\$ thus, \$\displaystyle k=-1\$.

Now for the check, the polynomial is \$\displaystyle x^2+x-6\$ which factors into \$\displaystyle (x+3)(x-2)\$ thus, it works.
Q.E.D.
• Jan 30th 2006, 04:13 PM
aussiekid90
Would this be the only possiblity because the problem states find all possible solutions for K
• Jan 30th 2006, 04:48 PM
ThePerfectHacker
Quote:

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.