A trinomial is an expression that contains 3 terms only. An example of a trinomial is a quadratic expression.

Ax²+bx+c = 0           Where a, b and c are real numbers

Case I: When a=1

When the coefficient of the term in x² is 1, we look 2 numbers such that the product is c and their sum or difference is b. We then write them down in factor form.

Example 1: Factorize x²+5x+6

Solution

X²+5x+6

X                     +2

X                     +3

X²+5x+6 = (x+2) (x+3)

Example 2: Factorize x²+7x+12

Solution

X²+7x+12

X                     +3

X                     +4

X²+7x+12 = (x+3) (x+4)

Case II: a¹1

When the coefficient of x² is not 1, we look for 2 numbers whose product is ac and whose sum is b. The trinomials into 4 terms and use the method of grouping to factorize it.