 Hello and welcome to the session. I am Neha and I am going to help you with the following question. The question says, factorize the expression q square minus 10q plus 21. Before proceeding for the solution, let's recall the identity x plus a into x plus b is equal to x square plus a plus b into x plus a b. This is the key idea for this question. Now let's see its solution. We have the expression q square minus 10q plus 21. Now if you look at the identity, then here we have two numbers a and b such that a plus b is the coefficient of x and a into b is the constant term. So here in the given expression the coefficient of q is minus 10 and constant term is 21. Here x is same as q. So that means we need to find two numbers a and b such that a plus b is equal to minus 10 and a into b is equal to 21. Now we know that 7 into 3 is equal to 21 and 7 plus 3 is equal to 10 but we need a plus b equal to minus 10. So that is only possible if we take both the numbers as negative minus 7 and minus 3. So let's take minus 7 and minus 3. Here minus 7 plus minus 3 is equal to minus 10 also minus 7 into minus 3 is equal to 21. So the given expression can be written as q is square minus 7q minus 3q plus 21. Now in first two terms the factor q is common and in the last two terms the factor 3 is common. So let's take q common from the first two terms and we are left with q minus 7. Now from the last two terms we will take minus 3 common and we are left with now we have taken minus sign common outside the bracket. That means signs inside the bracket will change. So we will get plus q minus 7. Now in these two terms the factor q minus 7 is common. So let's take it outside and we will get q minus 7 into q minus 3 which can also be written as q minus 3 into q minus 7. Thus the answer to this question is q minus 3 into q minus 7 in which q minus 3 and q minus 7 are the two factors of the given expression q is square minus 10q plus 21. With this we finished this session. Hope you must have enjoyed it. Goodbye, take care and keep smiling.