 Hello and welcome to the session. Let's discuss the following question. It says if the gcd of x square minus ax minus 6 and x square minus 2x plus b is x minus 6, find the values of a and b. Let's now move on to the solution and let px be equal to x square minus ax minus 6. Now we are given that x minus 6 is the gcd of the polynomial px. gcd means greatest common divisor of px. Now since it is a gcd therefore it is a factor of therefore x is equal to 6 is 0 using factor theorem. So now p at x is equal to 6 is 6 square minus 6 into a minus equal to 0. So this implies 36 minus 68 minus 6 is equal to 0 and this implies 30 minus 6 a is equal to 0 and this implies 30 is equal to 6 a. Dividing both sides by 6 we have a is equal to 5. Now again let qx be equal to x square minus 2x plus b. We are given that x minus 6 is the gcd qx therefore again q at x is equal to 6 is 0. So we have x square minus 2 into 6 plus b is equal to 0. So this implies 36 minus 12 plus b is equal to 0. So this implies 24 plus b is equal to 0. So this implies b is equal to minus 24. Value of a is the value of b is minus 24. So question and the session by for now take care have a good day.