 Hi and welcome to the session. Let's work out the following question. The question says find the LCM of the following polynomials 2xq minus 128 and x square minus 9x plus 20 x square minus 16. So these are the three polynomials given to us and we have to find their LCM. So let's start with a solution to this question. Left, Px be the first polynomial at this 2xq minus 128. This is equal to 2 into x cube minus 64. This is equal to 2 into x cube minus 4 cube because 64 is equal to 4 cube. That is equal to 2 into x minus 4 into x square plus 4x plus 16. Now this polynomial is equal to this because a cube minus b cube is equal to a minus b into a square plus b square plus a b. So this is equal to Px. That is this is the polynomial Px. Now let the second polynomial be qx. That is x square minus 9x plus 20. We factorize this now. This is equal to x square minus 5x minus 4x plus 20. And this is equal to x into x minus 5 because we have taken x common from these two terms minus 4 into x minus 5 because from here we have taken 4 common. Now this is equal to x minus 5 into x minus 4. Here we see that we have taken minus 4 common from these two terms. Now let polynomial Rx be equal to x square minus 16. This is equal to x square minus 4 square and this is equal to x minus 4 into x plus 4. Therefore, Lzm of the three polynomials Px, qx and Rx is equal to 2 into x minus 4 into x minus 5 into x plus 4 into x square plus 4x plus 16. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.