Introduction to trinomials

Trinomials are algebraic expressions that have only three terms. The three algebraic terms are separated by addition (+) or subtraction (-) signs. Each term is made up of a variable and a number.

Some examples of trinomials are

  • 2x2 + 3x + 4
  • a2 + 6b + 1
  • a + b + c
As you can see in the above examples, trinomials can have one, two or three variables.

If trinomials have only one variable, then their degree can not be lesser than 2; That is, it has to be a quadratic or a higher degree trinomial.

Factoring Quadratic Trinomials

Trinomials whose degree is 2 are called quadratic trinomials. These trinomials have a special importance in math. You can factor quadratic trinomials into a product of two lower degree expressions, and then you can get the roots of the trinomials by using the zero product rule.

Quadratic trinomials will help you learn advanced methods of factorization in mathematics.

One method to factor quadratic trinomials, and hence solve them, is by factoring the trinomials with the method of splitting the middle term. Let us go through factoring trinomials with the method of splitting the middle term to understand it better:

For example, consider the following quadratic trinomial:
x2 + 2x - 3
How can you factor the above trinomial? Look at the following steps to understand how you factor out trinomials:

Step 1: By the method of splitting the middle term, split the middle term of the trinomial as follows.
x2 + 3x - x - 3
Step 2: As you can see we have converted the trinomial into a four termed algebraic expression. Now take out the common factors of the first two and the last two terms of the trinomial.
x(x + 3) - 1(x + 3)
Step 3: As you can see we have (x + 3) as the common factor in the above expression. Thus factoring it out,
(x + 3)(x - 1)
Thus we factored the trinomials x2 + 2x - 3 into the product of two lesser degree trinomials (x + 3)(x - 1).

Conclusion on trinomials

As you can see, trinomials are factored by first converting them into four termed quadratic expressions, and then grouping is applied on these expressions two times. This factors the given trinomial into a product of two lesser degree algebraic expressions.

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