3. Factoring Trinomials

A trinomial is a 3 term polynomial. For example, 5x2 − 2x + 3 is a trinomial.

In many applications in mathematics, we need to solve an equation involving a trinomial. Factoring is an important part of this process. [See the related section: Solving Quadratic Equations.]

Example 1

Factor `x^2 − 5x − 6`

NOTE: Always check your answer by multiplying it out!

Example 2

Factor 2n2 − 13n − 7

Of course, after some practice, you will get a better sense of the numbers that will most likely work. It is unlikely that you will have to churn through all the possibilities before you find the right combination, like I have done above.

Now I'll show you a better method, one that reduces a lot of the guesswork.

Factoring by Grouping

This method requires the least amount of guessing and is recommended.

Example 3

Factor 6x2 + x − 12

NOTE: Of course, we may need to re-arrange our trinomial to get it into the correct form for grouping method to work. Normally this means we write our polynomial terms in decreasing powers of x.

Example 4

Let's return to Example 2 from above and do it again, but this time use grouping method.

Factor: 2n2 − 13n − 7

Exercises

Factorise each of the following:

(1) 3n2 − 20n + 20 [Care with this one!!]

(2) 3x2 + xy − 14y2

(3) 4r2 + 11rs − 3s2

(4) 6x4 − 13x3 + 5x2

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