[davide405]

I'm going to choose one problem, and work it out for you in exhaustive detail.Using number 7 as the example:14m^2 + 19mn - 3n^2Look at the first coefficient and the last coefficient, they are 14 and -3 respectively. Find the product of those two numbers. It is -42. Now consider the middle coefficient, 19.To begin to factor this trinomial, we need to find two numbers whose PRODUCT is -42, and whose SUM is 19.The two numbers that fit those requirements are 21 and -2. That is: 21(-2) = -41, and also 21 + (-2) = 19.Now, we need to re-write the trinomial, splitting up the middle term using the two numbers 21 and -2.14m^2 + 21mn - 2mn - 3n^2Now we need to group the terms by pairs.(14m^2 + 21mn) + (-2mn - 3n^2)Now we need to factor out the greatest common monomial factor from both pairs. For the first pair of terms, this is 7m. For the second pair of terms, this is -n.7m(2m + 3n) - n(2m + 3n)Notice that the binomials in the parentheses are identical. That makes them a binomial common factor. We can now "undistribute" the two monomials, and group them as a separate binomial.(7m - n)(2m + 3n)Good luck with your assignment!