# What is the new AC Method to factor trinomials?

##### 1 Answer

#### Answer:

Use the new AC Method.

#### Explanation:

**Case 1.** Factoring trinomial type

The factored trinomial will have the form:

The new AC Method finds

- The product
#p*q = a*c# . (When#a = 1# , this product is#c# ) - The sum
#(p + q) = b# - Application of the rule of Signs for real roots.

**Reminder of the Rule of Signs.**

- When
#a and c# have different signs,#p and q# have opposite signs. - When
#a and c# have the same sign,#p and q# have the same sign.

**New AC Method.**

To find **Rule of Signs** . The pair whose sum equals to

**Example 1.** Factor

**Solution.**

Factoring form:

.

**CASE 2** . Factor trinomial standard type

**Bring back to Case 1.**

Convert

Then divide

**Example 2** . Factor

**Converted trinomial:**

**Back to the original trinomial (1):**

**Factoring form**

This new AC Method avoids the lengthy factoring by grouping.