Factoring Quadratic Trinomials - 1

Factoring Trinomials of the form  x² + ax + b

To understand factoring polynomials we need to understand how to factor quadratic trinomials. We will do it in steps.

Trinomials are the polynomials with three terms.

Trinomials of the form x² + ax + b are called quadratic trinomials.

First term x² is called the quadratic term (having variable with degree 2). The coefficient of the quadratic term is 1; actually the quadratic term is 1x² (when 1 is the coefficient then it is never written but is understood that it’s there.)

Second term is "ax" and is known as linear term and “a” is the coefficient whose value is a natural number i.e. a = 1, 2, 3, 4……….

Third term b is known as the constant term and again b is a natural number i.e. b = 1, 2, 3, 4………..

It’s very easy to factor quadratic trinomials of the form x² + ax + b. We will do it by taking an example. Let’s factor x² + 6x + 8

So we have replaced “a” with “6” and “b” with “8”. Remember we only need to focus on these two numbers. 

We factor all such trinomials in two steps:

1.    Start to find the factor pairs of the constant term (b = 8)

2.    Pick a factor pair whose sum (total) is equal to the coefficient of the linear term (a = 6).

So let’s find a factor pair of 8 having a total of 6.

      1 . 8 = 8   (Always start with 1 times the constant term)

      2 . 4 = 8

      8 . 1 = 8 (We need not to write the last pair as it is same as the first pair. In other words when you see repeating factor pairs stop there).

Now see which factor pair has a total 6 (the coefficient of linear term). Obviously it is 2 . 4, hence we have find our factors which will be (x + 2) (x + 4) or we can write them alternatively as (x + 4) (x +2).

Write your answer as shown below:

    x² + 6x + 8

= (x + 2) (x + 4)

Now you factor the following quadratic trinomials

1.    x² + 3x + 2

2.    x² + 9x + 14

3.    x² + 9x + 8

4.    x² + 9x + 20

5.    x² + 9x + 18

   Following is the explanation to do it easily"