 Hi, welcome to the session. I'm Shashi. I'm going to help you to solve 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 square plus 3x plus 1 and the second polynomial is 3x raised to the power 4 plus 5x raised to the power 3 minus 7x square plus 2x plus 2. Let us first understand 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 our dividend is equal to 3x raised to the power 4 plus 5x cube minus 7x square plus 2x plus 2 and our divisor is equal to x square plus 3x plus 1. Let us now start the division. Since the first term of the dividend is 3x raised to the power 4, so we will multiply the divisor by 3x square to obtain the desired term. Multiplying the divisor by 3x square, we get 3x raised to the power 4 plus 9x cube plus 3x square. Now, subtracting the like terms and bringing down rest of the terms, we get minus 4x cube minus 10x square plus 2x plus 2. Now to obtain minus 4x cube, we will multiply x square with minus 4x. We get minus 4x cube minus 12x square minus 4x. Now, subtracting the like terms and bringing down rest of the terms, we get 2x square plus 6x plus 2. Now we will multiply divisor with 2 to get the term 2x square. Multiplying the divisor with 2, we get 2x square plus 6x plus 2. Now, again changing the signs and subtracting the like terms, we get remainder equal to 0. Since remainder is 0 implies x square plus 3x plus 1 is a factor of 3x raised to the power 4 plus 5x cube minus 7x square plus 2x plus 2. Caution is equal to 3x square minus 4x plus 2 and remainder is equal to 0. Therefore, we get x square plus 3x plus 1 is a factor of 3x raised to the power 4 plus 5x cube minus 7x square plus 2x plus 2. This completes the session. Hope you like the session. Bye-bye.