What are some methods for factoring a trinomial?

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

Take note that factoring is the reverse of multiplying.

So to factor trinomials, like quadratic expressions in the form ax^2 + bx + c, we may apply the reverse of FOIL. This method works when "a" is 1.

For example: `x^2 + 7x + 12`

Its factor will have a form:

( ___ ___ ) ( ___ ___ )

For the first term in each parenthesis, it refers to the factor of x^2.


(x ___ ) (x ___ )

For the last term in each parenthesis, it refers to the factor of 12.

However, if we add the pair factor, the sum should be equal to 7.

The pair factors of 12 are:

> 2,6

> -2,-6

> 3,4

> -3, -4

> 1, 12

> -1, -12

Among them, the pair factor that has a sum equal to 7 is 3 and 4. So, these two numbers are the last terms of each parenthesis.

(x + 3)(x + 4)

Therefore,  `x^2+7x+12=(x+3)(x+4)` .

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

To factor a trinomial/quadratic, there are 2 main ways you can go about it. The first would be to factor, or "reverse foil", where you find the factors that multiply out to be your trinomial. For example, if your had the equation x^2+5x+6 you know that x times x is x^2. 

(x    )(x    )

Then you find the two numbers that multiply to make 6 and add to make 5.


The second way is to use the quadratic formula. The formula is x = [ -b ± √(b2-4ac) ] / 2a, where you plug in your numbers from your equation(ax^2+bx+c).

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