Factoring Complex Trinomials

A complex trinomial, like a simple trinomial is also in the form of ax^2+ bx + c, but there is one difference: unlike a simple trinomial, a complex trinomial has an a-value greater than 1, which is why we cannot solve a complex trinomial like we would a simple trinomial. So, let us see how we can solve it:

Let’s do an example…

Factor the following: 2x^2 – 2x – 40

Step # 1: Multiply the a-value with the c-value. When we do that we get

-80(2 x -40).

Step # 2: Find two numbers, that when multiplied together equal the product from the first step (-80) but also when added together equal the middle term in the original equation, which is -2. In our case these numbers are -10 and 8.

**To learn how to find these factors, refer to the lesson on factoring simple trinomials**

Step #3: Rewrite the original equation, making sure to replace the middle term with the two terms whose coefficients are the numbers of -10 and 8.

2x^2 – 2 – 40

= 2x^2 – 10x + 8x – 40

Step #4: Common factor the first two terms in the above equation, and then common factor the last two terms. Make sure you factor the pairs separately since they will both have different factors.

= 2x(x-5) + 8(x-5)

Step #5: As you can see although the numbers in front of the brackets don’t match, the brackets do. So, put the common factor in its own bracket and then put the numbers in front of the bracket in their own bracket.

= (2x+8)(x-5)

Now you try…

Factor the Following: 3x^2 -13x + 12

Answer…

(3x-4)(x-3)

Extra Practice…

A Video for Extra Help…