 Hi and welcome to the session. My name is Shashi. I'm going to help you to solve the following question. The question is, divide the polynomial px by the polynomial gx and find the quotient and remainder. The polynomial is x raised to the power 4 minus 5x plus 6 is equal to px and the other polynomial gx is equal to 2 minus x square. First of all, you should know that dividend is equal to divisor multiplied by quotient plus remainder. This is the key idea to solve this question. Let us start with the solution now. We know dividend given in the question is equal to x raised to the power 4 minus 5x plus 6 and the divisor is equal to 2 minus x square or we can write it as minus x square plus 2 after rearranging it in the decreasing order of its degree. As we can see, the first term of our dividend is x raised to the power 4 so to get this term we will multiply the divisor with minus x square. Multiplying divisor with minus x square we get x raised to the power 4 minus 2x square. Now, subtracting the like terms and bringing down the rest of the terms of the dividend we get 2x square minus 5x plus 6. We have arranged all the terms in decreasing order of their degrees. Now our first term is 2x square so we will multiply the divisor with minus 2 to get the first term as 2x square. Multiplying divisor with minus 2 we get 2x square minus 4. Now again we will subtract the like terms and bring down the rest of the terms. Always remember to change the signs while subtracting we get minus 5x plus 10 since the degree of the remainder is less than the degree of the divisor therefore we will stop the division here itself. Now we can see that remainder is equal to minus 5x plus 10 and the quotient is equal to minus x square minus 2. So our required answer is quotient qx is equal to minus x square minus 2 and remainder rx is equal to minus 5x plus 10. This completes the session. Hope you like the session. Bye-bye.