EDGE Math 8

Factoring Other Trinomials

Trinomials in the Form $x^{2} + (a + b) x + a b$

When factoring a trinomial in the form $x^{2} + c x + d,$ where c and d are integers, find first two integers (say a and b) whose product is d and whose sum is c. If these integers exist then the trinomial can be factored as follows:

x^{2} + (a + b) x + a b = (x + a) (x + b) .

For example, suppose you need to factor $x^{2} + 4 x - 21.$ Observe that

x^{2} + 4 x - 21 = x^{2} + 4 x + (- 21) .

You need to find two integers whose product is $- 21$ (which means that one of the integers is positive and the other is negative) and whose sum is 4. You can check that these integers are –3 and 7. Thus,

x^{2} + 4 x - 21 = [x + (- 3)] (x + 7)

= (x - 3) (x + 7)