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.]
Factor x2 − 5x − 6
NOTE: Always check your answer by multiplying it out!
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.
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.
Let's return to Example 2 from above and do it again, but this time use grouping method.
Factor: 2n2 − 13n − 7
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