Tutoring math, you visit this topic with your grade 10 & 11 students.  The math tutor shows one method.

A complex trinomial is of the form

ax² + bx + c,

where a≠0,1.  An example is 2x² -3x -35. How do you factor such a trinomial?

Well, first of all, the easy trinomial method won’t work for a complex trinomial. Let’s see, now, what will:

Example: Factor 2x² – 3x – 35

Step 1: Multiply the lead coefficient (2 in this case) by the constant term (-35 in this case) to get -70.

Step 2: Find two numbers that multiply to make the product from step 1, but add to make the middle term coefficient (-3, in this case). Therefore, for our example, we need find the two numbers that multiply to make -70 but add to make -3. Of course, the numbers are -10 and 7.

Step 3: Rewrite the original trinomial, replacing the middle term with two terms whose coefficients are the numbers from step 2.

In other words,

2x² -3x – 35 becomes

2x² -10x +7x -35.

Step 4

Common factor the first two terms from step 3. Then, common factor the last two. Do the pairs separately; it won’t be the same common factor for the first two as for the last two.

2x(x-5) + 7(x-5)

Step 5

Notice from Step 4 that, although the common factors you took out front don’t match, the brackets do match. Put the common factors in their own bracket, then rewrite:

(2x+7)(x-5)

Step 6 (optional): Foil out your answer from Step 5 to check it.

First: 2x(x)=2x²

Outer: 2x(-5)=-10x

Inner: 7(x)=7x

Last: 7(-5)=-35

Add the four terms:

2x² -10x +7x -35 = 2x² -3x -35

That’s one way to factor complex trinomials. Trial and error is faster; I’ll explore it in a future post:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.