 Hi and welcome to the session. Let us discuss the following question. Question is, divide the polynomial Px by the polynomial gx and find the quotient and remainder in each of the following. Px is equal to x raised to the power 4 minus 3x square plus 4x plus 5, gx is equal to x square plus 1 minus x. Let us now start the solution. We have d1 divided is equal to Px which is equal to x raised to the power 4 minus 3x square plus 4x plus 5 and divisor is equal to x square plus 1 minus x. We will divide x raised to the power 4 minus 3x square plus 4x plus 5 by x square plus 1 minus x. We know x square plus 1 minus x can be written as x square minus x plus 1. We have arranged all the terms in descending order of their degrees. So, we can write divisor is equal to x square minus x plus 1. Let us now start the division. First term of the dividend is x raised to the power 4. So, we will multiply x square by x square to get x raised to the power 4. Now, multiplying the divisor by x square we get x raised to the power 4 minus x cube plus x square. Now, we will subtract the like terms and rewrite the other terms of the dividend. We get x cube minus 4x square plus 4x plus 5. We have arranged all the terms in descending order of their degrees. Now, to get x cube we will multiply x square by x. So, multiplying the divisor by x we get x cube minus x square plus x. Now, we will subtract the like terms and rewrite the other terms of the dividend. Always remember to change the sign while subtracting. Now, we know x cube minus x cube is 0 minus 4x square plus x square would be equal to minus 3x square. Plus 4x minus x is equal to plus 3x and plus 5 is the other term of the dividend. Now, to get minus 3x square we will multiply the divisor by minus 3. So, we get minus 3x square plus 3x minus 3. Now, we will subtract the like terms. Now, we know minus 3x square plus 3x square is equal to 0 plus 3x minus 3x is again 0 plus 5 plus 3 is equal to 8. So, we get remainder is equal to 8 quotient is equal to x square plus x minus 3. So, we can write quotient is equal to x square plus x minus 3 and remainder is equal to 8. This is our required answer. This completes the session. Hope you understood the session. Goodbye.