 Hi and 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 t square minus 3 and the second polynomial is 2t raised to the power 4 plus 3t cube minus 2t square minus 90 minus 12. First of all we should 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 now start with the solution. We know dividend given to us in the question is 2t raised to the power 4 plus 3t cube minus 2t square minus 90 minus 12 and the divisor given in the question is equal to t square minus 3. Let us start the division now. We see that the first term of the dividend is 2t raised to the power 4 so we will multiply the divisor with 2t square to get the desired term. Multiplying the divisor with 2t square we get 2t raised to the power 4 minus 60 square. Now subtracting the right terms and rewriting the rest of the terms of the dividend we get 3t cube plus 4t square minus 90 minus 12. Now our first term is 3t cube so we will multiply the divisor with 3t. Multiplying 3t with the divisor we get 3t cube minus 90. Now subtracting the right terms and rewriting the rest of the terms of the dividend we get 4t square minus 2 means 4t square. So we will multiply t square with 4 to get the desired term so multiplying the complete divisor with 4 we get 4t square minus now subtracting the right terms we get remainder equal to 0. Our remainder is equal to 0 this implies t square 2t raised to the power 4 plus 3t cube minus 2t square minus 90 minus 12. Therefore quotient is equal to 2t square plus 3t plus 4 and remainder is equal to 0 plus 3t cube minus 2t square minus 90 minus 12 is the required answer. This completes the session. Hope you like the session. Take care and goodbye.