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Chapter Contents

• Factoring and Fractions
• 1. Special Products
• 2. Common Factor and Difference of Squares
• 3. Factoring Trinomials
• 4. The Sum and Difference of Cubes
• 5. Equivalent Fractions
• 6. Multiplication and Division of Fractions
• 7. Addition and Subtraction of Fractions
• 8. Equations Involving Fractions

• Comments, Questions?

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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

Answer

NOTE: Always check your answer by multiplying it out!

Here is a LiveMath document to illustrate this.

LIVEMath

Example 2:

Factor 2n² − 13n − 7

Answer

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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

Answer

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

Answer

Exercises

Factorise each of the following:

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

Answer

(2) 3x² + xy − 14y²

Answer

(3) 4r² + 11rs − 3s²

Answer

(4) 6x⁴ − 13x³ + 5x²

Answer