 Hi and welcome to the session. Let's work out the following question. The question says, find a and b so that the polynomials px equal to x squared plus 3x plus 2 into x squared plus 2x plus a and qx equal to x squared plus 7x plus 12 into x squared plus 7x plus b may have x plus 1 into x plus 3 as their hcf. Let us see the solution to this question. We have the polynomial px as x squared plus 3x plus 2 into x squared plus 2x plus a and qx as x squared plus 7x plus 12 into x squared plus 7x plus b. Since it is given that x plus 1 into x plus 3 is the hcf of px and qx. So, y at minus 3 will be minus 3 the whole square plus 3 into minus 3 plus 2 multiplied by minus 3 the whole square plus 2 into minus 3 plus a is equal to 0. This implies 9 minus 9 plus 2 into 9 minus 6 plus a is equal to 0. This implies 2 into 3 plus a is equal to 0. This implies a plus 3 equals to 0 or a is equal to minus 3 and we see that p at minus 1 will be minus 1 the whole square sorry this is q at minus 1. So, q at minus 1 will be minus 1 the whole square plus 7 into minus 1 plus 12 multiplied by minus 1 the whole square plus 7 into minus 1 plus b is equal to 0. This implies this is 1 minus 7 is minus 6 12 minus 6 is 6 so we have 6 into. Here also we will have minus 6 plus b equals to 0 and this implies that b is equal to 6. So, our answer to this question is a is equal to minus 3 and b is equal to 6. I hope that you understood the solution and enjoyed the session. Have a good day.