 Hi and welcome to the session. I am Asha and I am going to help you for the following problem which says factorize x cube minus 2x square minus x plus 2. So let us start with the solution and let px be the given polynomial which is equal to x cube minus 2x square minus x plus 2. Now we should look for all the factors of 2 and the factors of 2 are plus minus 1 and plus minus 2. So by grand method we will find the value of x by replacing plus minus 1 or plus minus 2 such that the value of the polynomial px comes out to be 0. So replacing x that is value 1 by 1 we will find that on replacing x by 2 we get the value of the polynomial as 0. Let us check out. So I am replacing x by 2 we have 2 cube minus 2 times of 2 whole square minus 2 plus 2 which is further equal to 2 cube minus 2 cube minus 2 plus 2. Now 2 cube minus 2 cube cancels out and minus 2 plus 2 cancels out and we have 0. So this implies pf 2 is equal to 0. So x minus 2 is a factor of px and so on dividing px by x minus 2 we will have the remainder as 0. So let us divide px which is x cube minus 2x square minus x plus 2 by x minus 2. Now first we will have to multiply it with x square or multiplying x square with x minus 2 we get x cube minus 2x square. Now on changing the signs these two cancels out and these two cancels out and we are left with minus x plus 2. Now we will have to multiply x minus 2 by minus 1 and so we get minus x plus 2. Now again in changing the signs we have the remainder as 0 and as we know dividend is equal to divisor into quotient plus remainder. So dividend is up px divisor is x minus 2 quotient is x square minus 1 and remainder is 0 and now since x square minus 1 is in the form of a square minus b square whose formula is a minus b into a plus b. So this can be written as x minus 1 into x plus 1. Thus px can be written as x minus 2 into x minus 1 into x plus 1 and that is one factorizing the given polynomial px which is x cube minus 2x square minus x plus 2 we get the factors as x minus 2 into x minus 1 into x plus 1. So this completes the solution hope you enjoyed this session take care and have a good day.