 Hello and welcome to the session. In this session, we shall discuss division of algebraic expressions. As some laws of exponents are used in the division of algebraic expressions, we will revise them. From the laws of exponents, we have x raised to power m divided by x raised to power n is equal to x raised to power m minus n, where m and n are positive integers, m is greater than n. Also, x raised to power n into x raised to power n is equal to x raised to power n plus n, where m and n are positive integers. To be above laws, we derive that x raised to power 0 is equal to 1. Let us now learn how to divide a monomial by a monomial. The rule followed is, first divide the numerical coefficients, then divide the variables using the laws of exponents, and then multiply the results obtained in the first two steps. Now, let us divide minus 56 a raised to power 7, b raised to power 4, c raised to power 3 by 8 a squared b squared c squared. In this, the first step is to divide the numerical coefficients, that is divide minus 56 by 8, then divide the variables using the laws of exponents discussed earlier. So here, a raised to power 7, b raised to power 4, c raised to power 3 is divided by a squared b squared c squared. Minus 56 by 8 is equal to minus 7 and a raised to power 7, b raised to power 4, c raised to power 3 divided by a squared b squared c squared is equal to a raised to power 7 minus 2, b raised to power 4 minus 2, c raised to power 3 minus 2, which is equal to a raised to power 5, b raised to power 2, c. Now, the third step is to multiply the two results, we get minus 7 into a raised to power 5, b raised to power 2, c, which is equal to minus 7 a raised to power 5, b raised to power 2, c. Now, let us see how a polynomial is divided by a monomial, divide each term of the polynomial individually by a monomial by using the rules of dividing monomial by a monomial. Consider the following example, divide 24 a squared b squared c squared plus 12 a b c by 3 a b. Let us solve this, 24 a squared b squared c squared plus 12 a b c by 3 a b is equal to 24 a squared b squared c squared by 3 a b plus 12 a b c by 3 a b, which is equal to 8 a raised to power 2 minus 1, b raised to power 2 minus 1, c raised to power 2 minus 0 plus 4 a raised to power 1 minus 1, b raised to power 1 minus 1, c raised to power 1 minus 0, which is equal to 8 a b c raised to power 2 plus 4 c raised to power 0 is equal to 1 and b raised to power 0 is equal to 1. To study the division of two polynomials, we will take an example and go through these steps that is to divide 14 minus 17 x plus 5 x square by x minus 2. We shall follow the following steps. Step one is to set up a long division form and arrange the polynomials in descending order leaving space for the missing terms. We get x minus 2 is divided by 5 x square minus 17 x plus 14. Step two is to divide the first term of the division that is 5 x square by the first term of the divisor that is x and write the quotient in this way. That is when we divide 5 x square by x, we get 5 x plus 3 is to multiply the first term of the quotient that is 5 x by each term of the divisor that is x minus 2 that is 5 x into x minus 2 is equal to 5 x square minus 10 x and write it below the dividend. Step four is subtract like terms and bring down the other left out terms. Now use the remainder minus 7 x plus 14 as the new dividend and repeat steps 2 to 4. We get x minus 2 is divided by minus 7 x plus 14. The quotient is minus 7 and minus 7 into x minus 2 is equal to minus 7 x plus 14. Now after subtraction we get the remainder as 0. Step six is to stop when the remainder becomes 0 or there is no term in the remainder into which the first term of the divisor will divide evenly. So the full solution is now we can also verify this by using the formula dividend is equal to divisor into quotient plus remainder by substituting values in the right hand side of the formula we get x minus 2 into 5 x minus 7 plus 0 which is equal to 5 x square minus 17 x plus 14 which is the dividend hence solution is correct. Let us discuss how brackets are removed from a polynomial. Expressions consisting of a list of brackets must be removed in a particular order as follows by parenthesis curly brackets and then square brackets. A bracket with a plus sign before it may be removed without changing the sign of any term and if there is a minus sign then the signs inside the bracket are changed when there is a term before the bracket. The bracket is removed by multiplying it with every term in the bracket. In this expression we first solve the innermost bracket that is we multiply minus 2 by 4 x minus 1 that is the expression will become 5 x plus 3 minus 4 x minus 2 x minus 8 x plus 2. Now we solve the curly brackets and we obtain 5 x plus 3 minus 4 x minus minus 6 x plus 2. Now we will open the curly brackets and we get 5 x plus 3 minus 4 x plus 6 x minus 2. Now we will solve the square bracket and we get 5 x plus 3 minus minus 2 which can be written as 5 x plus 3 minus 10 x plus 2. On further solving we get minus 5 x plus 5. This is the final answer. This completes our session. Hope you enjoyed this session.