1. What is the AC Method?

The AC method is a technique for factoring quadratic expressions of the form \( ax^2 + bx + c \). It's particularly useful when the leading coefficient \( a \) is not 1. The method gets its name from the first step: multiplying \( a \) and \( c \) to find factor pairs.

2. How the AC Method Works

The AC method follows these steps:

Example: For \( 6x^2 + 7x - 3 \):

• \( a \times c = 6 \times -3 = -18 \)
• Find factors: 9 and -2 (since 9 × -2 = -18 and 9 + -2 = 7)
• Rewrite: \( 6x^2 + 9x - 2x - 3 \)
• Group: \( (6x^2 + 9x) + (-2x - 3) = 3x(2x + 3) -1(2x + 3) \)
• Result: \( (2x + 3)(3x - 1) \)

3. When to Use This Method

Best for: Quadratics where \( a \neq 1 \) and the expression can be factored using integers. When the quadratic doesn't factor nicely with integers, you may need to use the quadratic formula instead.

4. Using the Calculator

Tips: Enter integer coefficients a, b, and c from your quadratic \( ax^2 + bx + c \). The calculator will show the step-by-step factoring process or indicate if the quadratic can't be factored with this method.

5. Frequently Asked Questions (FAQ)

Q1: What if the quadratic can't be factored?
A: The calculator will notify you. In such cases, you may need to use the quadratic formula or complete the square.

Q2: Does this work for all quadratics?
A: The AC method only works for factorable quadratics with integer coefficients. Some quadratics require other methods.

Q3: Why is it called the AC method?
A: Because the first step involves multiplying the coefficients \( a \) and \( c \) (the first and last terms).

Q4: Can I use this for simple factoring?
A: Yes, but when \( a = 1 \), the simpler "find two numbers that multiply to \( c \) and add to \( b \)" method is usually faster.

Q5: What about special cases like perfect squares?
A: The AC method will still work, but recognizing perfect square trinomials or difference of squares can provide shortcuts.