 Hello and welcome to the session. In this session we discussed the following question which says, find the quotient and remainder when 10a cube minus 4a plus 1 minus 5a square plus 8a4 is divided by a minus 1 plus 2a square. Let's move on to the solution. We need to divide 10a cube minus 4a plus 1 minus 5a square plus 8a4 by a minus 1 plus 2a square. First of all, we need to arrange the terms of the divisor and the dividend in descending order of their degrees. So, on arranging them we get 8a4 plus 10a cube minus 5a square minus 4a plus 1 divided by 2a square plus a minus 1. So, we have written the dividend here and the divisor here. Now, we divide these two polynomials. First, we divide the first term of the dividend that is 8a4 by the first term of the divisor which is 2a square. This gives us 4a square. Now, we multiply this 4a square with each and every term of the divisor. So, we get 8a4 plus 4a cube minus 4a square and we subtract this expression from this expression. So, this would give us 6a cube minus a square. Now, we take down these two terms minus 4a plus 1. Now, this is our new dividend that is 6a cube minus a square minus 4a plus 1. Now, we divide the first term of this dividend that is 6a cube by the first term of the divisor that is 2a square. We get plus 3a and we write it in the question. Now, we multiply this term plus 3a with each and every term of this divisor. So, this gives us 6a cube plus 3a square minus 3a. We subtract this expression from this new dividend. So, this would give us minus 4a square minus a plus 1. Now again, minus 4a square minus a plus 1 is our new dividend. We divide the first term of this new dividend that is minus 4a square by the first term of the divisor that is 2a square and this gives us minus 2 in the quotient. We multiply this minus 2 with each and every term of this divisor to give us minus 4a square minus 2a plus 2 and we subtract this from the expression minus 4a square minus a plus 1. So, this gives us a minus 1. Now, this polynomial a minus 1 has degree less than that of the divisor. So, we will stop here only. So, this is the quotient and this is the remainder plus we have the quotient is 4a square plus 3a minus 2 and the remainder is a minus 1. So, this is our final answer. This completes the session. Hope you have understood the solutions of this question.