The AC Test: Determining If A Certain Trinomial Is Factorable

The AC Test : Determining If A Trinomial Is Factorable

In factoring quadratic trinomials, it is important we know how to determine if a certain trinomial is factorable.In doing this, we use the AC test. In this hub I present several examples to show how the AC test work.

Example One :Is 10X^2 – 17X + 6 factorable ?

A is the coefficient of X^2 while C is the constant or the third term of the trinomial.We get the product of A and C. In this case A = 10 andC = 6. The product is 60. Then list down all the factors of 60 :

(6)(10)(-6)(-10)(5)(12)(-5)(-12)

Then add the factors by pair and check if the sum will be equal to the coefficient of the middle term of the given trinomial.

-5 + -12=-17this is equal to the coefficient of the middle term therefor ethe given trinomial 10X^2 -17X + 6 is factorable. And its factors are (5X -6) (2X – 1).

Example Two :Is 2X^2 –XY -28Y^2 factorable ?

Step One : Get the product of AC.A = 2 and C = -28 therefore AC = -56

Step Two : List down factors of -56.

(-8)(7)(-7)(8)(28)(-2)(2)(-28) (-14)(4)(-4)(14)

We can see that -8 + 7= -1. -1 is the coefficient of the middle term. Therefore the given trinomial 2X^2 –XY -28^2 is factorable, Its factors are (2X + 7) (X – 4).

Example Three :Is 2X^2 +9X -9 factorable ?

Step One : Get product of AC. A =2 and C = -9 therefore AC= -18.

Step Two : List down Factors of -18.

(9)(-2)(2)(-9)(-3)(6)(-6)(3)(18)(-1)(1)(-18)

No sum will be equal to +9 therefore the trinomial 2X^2 + 9X -9 is not factorable.