 Hello and welcome to the session. In this session we discussed the following question which says, find the hcf of 16xq minus 4x square minus 30x, 32x to the power 4 minus 50x square and 4x square plus 9x plus 5. Let's proceed with the solution now. We are given three polynomials and we need to find the hcf of these polynomials. We have the first polynomial 16xq minus 4x square minus 30x. Our first step to find the hcf of these three polynomials would be to find the factors of the polynomials. So we consider the first polynomial first and now we find the factors of this polynomial. Now 2x is common in this polynomial so we take 2x out as a common factor of the three terms. Inside the bracket we are left with 8x square minus 2x minus 15. Now next we will factorize the polynomial 8x square minus 2x minus 15. So this would be 8x square minus 12x plus 10x minus 15. Then next 2x the whole multiplied by. Now we will take the common factors out of 8x square and 12x. So we have 4x and inside we are left with 2x minus 3. Now from these two terms that is 10x and minus 15 we take out the factor plus 5 and inside we are left with 2x minus 3. So this is equal to 2x the whole multiplied by 2x minus 3 into 4x plus 5. So we have that our first polynomial 16x cube minus 4x square minus 30x is equal to 2x into 2x minus 3 the whole multiplied by 4x plus 5 the whole. So we have factorized the first polynomial. Now let's consider the second polynomial which is 32x to the power 4 minus 50x square. Now we will find the factors of this polynomial 2x square is a common factor of the two terms. So we take 2x square outside and inside the brackets we are left with 16x square minus 25. So further we get this is equal to 2x square whole multiplied by 4x the whole square minus 5 square this is equal to 2x square the whole multiplied by. Now we will factorize this using the identity a square minus b square equal to a plus b the whole multiplied by a minus b. So we get this as 4x plus 5 the whole multiplied by 4x minus 5. So we get this is equal to 2x square multiplied by 4x plus 5 the whole multiplied by 4x minus 5. This is the polynomial 32x to the power 4 minus 50x square. So we have got the factors of this polynomial also. Now consider the third polynomial which is 4x square plus 9x plus 5 now we will find the factors of this polynomial this is equal to 4x square plus 4x plus 5x plus 5. So further we get 4x the whole multiplied by x plus 1 plus 5 the whole multiplied by x plus 1 which is equal to 4x plus 5 the whole multiplied by x plus 1. So these are the factors of the polynomial 4x square plus 9x plus 5. Now that we have found out the factors of the three polynomials we will next find out the common factors of the three polynomials. As you can see only the factor 4x plus 5 is common in all the three polynomials that is the common factor to all the polynomials is 4x plus 5. So we say that the xcf of the given polynomials is 4x plus 5. So hence 4x plus 5 is our final answer. This completes the session hope you have understood the solution of this question.