 Welcome to our session. Let us discuss the question. The question says find the gcd of polynomials 12 into x cube plus x square plus x plus 1 and 18 into x to the power 4 minus 1. Now we begin with the solution. Let fx is equal to 12 into x cube plus x square plus x plus 1 and gx is equal to 18 into x to the power 4 minus 1. Now in the first step we will write fx and gx as product of reducible factors plus 1 but where it can be written as 2 into 2 is expression common from the first two terms and one common from the last two terms. This is equal to minus 1. Now 18 is equal to x to the power 4 minus 1 can be written as x square minus 1 into x square a square minus b square e into 3 into x square minus 1 is equal to x minus 1 into x plus 1 into x square.