Factorizing Trinomials with a=1 Lesson

A lesson on factorizing trinomials with leading coefficient 1. The students are first asked to multiply out pairs of brackets containing linear polynomials. Then they are asked to make some observations. They are expected to observe that in the trinomial obtained after multiplying out the brackets the coefficient of x is the sum of the numbers in the brackets and the constant term is their product. Then they are asked to generalize that for any pair of linear polynomials. Once this result has been established, they are given some trinomials with leading coefficient equal to one and are asked to factorize them. In this exercises they must work in the converse way, they must try to find pairs of numbers whose product and sum equal the coefficients of the given polynomial. Finally, there is an exercise on signs, including the four possible combinations of signs for the product and sum of the trinomial. Detailed solutions are provided.