 Hello and welcome to the session. In this session we discussed the following question which says divide 3x cube minus 5x square plus 10x minus 3 by x plus 1 and verify the result. So here we have to divide a polynomial by another polynomial. Let's move on to the solution so we have to divide the polynomial 3x cube minus 5x square plus 10x minus 3 by the polynomial x plus 1. Now here first we will arrange the two polynomials in descending powers of x. As you can see both the polynomials are arranged in descending powers of x. So here we have the divisor that is x plus 1 and the dividend 3x cube minus 5x square plus 10x minus 3. Now first we will divide the first term of the dividend that is 3x cube in this case by the first term of the divisor which is x and we write the quotient here. So when we divide 3x cube by x we get 3x square. So we would write 3x square here. Now next we will multiply the first term of the quotient that is 3x square by each term of the divisor and we write the product below the dividend. So 3x square multiplied by x gives us 3x cube and we write 3x cube below 3x cube. Then 3x square multiplied by 1 gives us 3x square and we write plus 3x square below minus 5x square. Now next we will subtract the like terms so we get minus 8x square. Now we write the remaining terms of the dividend here that is plus 10x minus 3. Now this would be the new dividend and this is the divisor. Again we would follow the same steps for division that is we will divide the first term of the new dividend that is minus 8x square by the first term of the divisor which is x. Now minus 8x square divided by x gives us minus 8x. We write minus 8x to be right of 3x square in the quotient. Now we multiply minus 8x with each term of the divisor and we write the product below the new dividend. So minus 8x multiplied by x gives us minus 8x square and we write it below minus 8x square. Then minus 8x multiplied by 1 gives us minus 8x which we write below 10x. Now we subtract the like terms so we get 10x plus 8x which is 18x. We bring down this minus 3 with 18x. Now this is our new dividend and this is our divisor. Again in the same way we divide the first term of this new dividend that is 18x by the first term of the divisor which is x. So 18x when divided by x gives us 18. We write this 18 to be right of minus 8x in the quotient. Now we multiply 18 with each term of the divisor. 18 multiplied by x gives us 18x. We write 18x below 18x and 18 multiplied by 1 gives us 18. So we write 18 below minus 3 and now we subtract the like terms. So we get here minus 21. Now since minus 21 is not evenly divided by x that is the first term of the divisor. So we would stop here itself. Thus we get minus 21 as the remainder and this is the quotient. Thus we have the quotient is 3x square minus 8x plus 18 the remainder is minus 21. So this gives us the answer. This is the quotient and this is the remainder. Now since we are supposed to verify this result so we will do the verification for this. We have to show that dividend is equal to divisor multiplied by quotient plus remainder. This is what we have to show to do the verification of the result. Now first of all let's consider divisor multiplied by the quotient plus the remainder. Now in this case the divisor is 3 further equal to plus 1 multiplied by the quotient which is x square minus 8x plus 18 and the which is minus 21. Now we will multiply these two polynomials. So this is equal to 3x cube minus 8x square plus 18x plus 8x plus 18 minus 21. Further we get 3x cube minus 8x square plus 3x square gives us minus 5x square then plus 18x minus 8x plus 18 minus 21 is minus 3. Now divisor into quotient plus remainder is equal to 3x cube minus 5x square plus 10x minus 3 the dividend. Here we have divisor remainder is equal to the dividend. The result is hope you have understood the solution of this question.