Mini Lesson Question
Question #2: Factor Trinomials
Factor Trinomials
Example 1
To factor the trinomial , you can reverse the process of FOIL.
The trinomial factors to two binomials of the form .
- Using FOIL: .
- Using the distributive property: .
Take a look at the trinomial :
To factor the trinomial, we need factors of 12, and , so that the sum, , is 8.
Use a table to find all the different combinations of factors of 12. Then, find the sum of the factors.
Factors of 12 | Sum of factors |
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The numbers 2 and 6 have a product of 12 and a sum of 8. They are the factors we need:
Example 2
Factor the trinomial .
To factor the trinomial, we need factors of -24, and , so that the sum, is -5.
- The product of the factors is negative, so the factors must have opposite signs.
- The sum is negative, so the negative sign will go with the factor with the greater absolute value.
Factors of 12 | Sum of factors |
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The numbers 3 and -8 have a product of -24 and a sum of -5.
Example 3
Factor the trinomial .
To factor the trinomial, we need factors of 18, and , so that the sum, , is -9.
- The product of the factors is positive, so the factors must have the same signs.
- The sum is negative, so both factors are negative.
Factors of 18 | Sum of factors |
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The numbers -3 and -6 have a product of 18 and a sum of -9.
Try it
Factoring Trinomials
Factor the trinomial .
Here is how to factor the trinomial .
To factor the trinomial, we need factors of -24, and , so that the sum, , is 2.
- The product of the factors is negative, so the factors must have opposite signs.
- The sum is positive, so the greater factor is positive.
Factors of 24 | Sum of factors |
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The numbers 6 and -4 have a product of -24 and a sum of 2.
Check Your Understanding
Factor: .
Check yourself: To factor the trinomial, we need factors of 36 that sum to – 13.
- Our factor pairs could be: 1 & 36, 2 & 18, 3 & 12, 4 & 9, 6 & 6
- Because 36 is positive, we know the factors will have the same sign.
- Since the sum is negative, both of the factors must be negative.
The factor pair that sums to 13 are 4 & 9, so our binomials are
Video: Factoring Trinomials
Watch the following video to learn more about factoring trinomials.
Khan Academy: Factoring Quadratics