# 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.**