# 3. Factoring Trinomials

A **trinomial** is a **3 term polynomial.** For example, 5*x*^{2} − 2*x* + 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 2*n*^{2} − 13*n* − 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 6*x*^{2} + *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: 2*n*^{2} − 13*n* − 7

### Exercises

Factorise each of the following:

**(1)** 3*n*^{2} − 20*n *+ 20** [Care with this one!!]**

**(2)**** **3*x*^{2} + *xy *− 14*y*^{2}

**(3)** 4*r*^{2} + 11*rs ** *− 3*s*^{2}

**(4)** 6*x*^{4} − 13*x*^{3} + 5*x*^{2}

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