In your own words explain the process of factoring a trinomi

In your own words, explain the process of factoring a trinomial with a leading coefficient that is not equal to one. Why is this process more difficult than when the leading coefficient is equal to one? How could you verify your answer? For this DQ, complete the problem provided by your instructor.

Solution

To begin with, we write the trinomial in the descending order from the highest power to the lowest power. We scrutinize the trinomial to ascertain whether the three terms have something in common (i.e. the greatest common factor- GCF). If yes, we separate the GCF as a factor. Then we multiply the leading coefficient by the constant term. We make a list of the factors from the previous step and ascertain the combination of numbers which can be combined to get the number next to x. After taking a decision about the pair of numbers from the list, we assign a sign to each number so that when these are combined, these will equal the number next to x and also their product equals the product of the leading coefficient and the constant term. Then we break the original expression into four terms by breaking the middle term into two terms as ascertained in the previous step. Now, we can factor by grouping. It may be observed that the GCF, if any, will be a factor.