 Hi and welcome to the session. I am Shashini and I am going to help you with the following question. Question is, check whether the first polynomial is a factor of second polynomial by dividing the second polynomial by the first polynomial. First polynomial is x cube minus 3x plus 1 and second polynomial is x raise to the power 5 minus 4x cube plus x square plus 3x plus 1. First of all, we should know that the first polynomial is a factor of second polynomial if on dividing the second polynomial by the first polynomial the remainder is 0. This is the key idea to solve this question. Let us start with the solution now. We know dividend is equal to x raise to the power 5 minus 4x cube plus x square plus 3x plus 1 and our divisor is equal to x cube minus 3x plus 1. Let us start the division now. We can see first term of the dividend is x raise to the power 5 so we will multiply x cube with x square to get x raise to the power 5. Now multiplying x square with the divisor we get x raise to the power 5 minus 3x cube plus x square. Now subtracting the light terms and rewriting the rest of the terms of the dividend we get minus x cube 3x plus 1. Now our first term is minus x cube so we will multiply the divisor with minus 1 to get the desired term. Multiply the divisor with minus 1 we get minus x cube minus 1. Now subtracting the light terms we get the remainder equal to since the remainder is not equal to 0 we get x1 is not a factor of x raise to the power 5 minus 4x cube plus x plus 1. Our quotient is equal to x square minus 1. Reminder is since remainder is not equal to 0 so x cube minus 3x plus 1 is not a factor of x raise to the power 5 minus 4x cube plus x square plus 3x plus 1. So our final answer is no understood the session good