 Hi and welcome to the session, let's work out the following question. The question says, X squared plus X minus 2 is the GCD of the expressions X minus 1 into 2X squared plus AX plus 2 and X plus 2 into 3X squared plus BX plus 1 find the values of A and B. So let us see the solution to this question. First of all we see that X squared plus X minus 2 is equal to X plus 2 into X minus 1. Now let the polynomial PX be X minus 1 into 2X squared plus AX plus 2 since X plus 2 is a factor of PX therefore P at minus 2 should be equal to 0 by the factor theorem. This implies minus 2 minus 1 into 2 into minus 1 the whole square minus 2A plus 2 sorry this will be 2 into minus 2 the whole square plus A into minus 2 plus 2 should be equal to 0. This implies minus 3 into 8 minus 2A plus 2 should be equal to 0 or we can say minus 3 into 10 minus 2A should be equal to 0. This implies minus 30 plus 6A is equal to 0 this implies 6A is equal to 30 this implies that A is equal to 5. Now let the polynomial QX be equal to X plus 2 into 3X squared plus BX plus 1 since X minus 1 is a factor of QX. This implies Q at 1 should be equal to 0 again by the factor theorem. This implies 1 plus 2 into 3 plus B plus 1 is equal to 0 this implies 3 into 4 plus B should be equal to 0. This implies 12 plus 3 B should be equal to 0 this implies B should be equal to minus 4. So our answer to this question is that A is equal to 5 B is equal to minus 4. So I hope that you understood the solution and enjoyed the session have a good day.