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 x2 − 5x − 6
NOTE: Always check your answer by multiplying it out!
Here is a LiveMath document to illustrate this.
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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