 Hello and welcome to the session, let's work out the following problem. It says find the value of k so that x minus 1 is a factor of k square x square minus 2 kx minus 3. So let's now move on to the solution, let px be this polynomial k square x square minus 2 kx minus 3. Now we are given that x minus 1 is a factor of px. Now since x minus 1 is a factor of px therefore p of 1 is 0 by factor theorem. Now p of 1 is k square 1 square minus 2k into 1 minus 3 is equal to 0. So we have k square minus 2k minus 3 is equal to 0. Now this is a quadratic equation in k and now we'll solve this for k. So now we factorize this k square minus 3k plus k minus 3 is equal to 0 taking k common from the first two terms we have k minus 3 plus 1 k minus 3 is equal to 0 k plus 1 into k minus 3 is equal to 0. So this implies k plus 1 is equal to 0 or k minus 3 is equal to 0 and this implies k is equal to minus 1 or k is equal to 3 hence k is equal to minus 1 or 3. So this completes the question and the session. Bye for now. Take care. Have a good day.