Final answer:
The AC method requires a quadratic polynomial in the form ax^2 + bx + c with a not equal to 1 and involves multiplying a and c to find a product, then using this to break down the middle term and factor by grouping.
Step-by-step explanation:
The AC method of factoring requires the polynomial to be a quadratic equation in the form ax^2 + bx + c, where a, b, and c are constants, and a is not equal to 1. This method is used to factor second-degree polynomials, more commonly known as quadratic polynomials, in which the leading coefficient (the coefficient of x^2) is greater than 1.
To factor by the AC method:
Multiply a (the coefficient of x^2) and c (the constant term) to find the product AC.
Find two numbers that multiply to AC and add to b (the coefficient of x), the middle term.
Rewrite the middle term as the sum of the two numbers found in step 2, creating four terms.
Factor by grouping by pairing the terms and finding the common factors of each pair.
Simplify to find the factors of the original polynomial.
Example:
Factor 2x^2 + 7x + 3.
For the polynomial 2x^2 + 7x + 3:
AC = 2*3 = 6.
The numbers that multiply to 6 and add up to 7 are 1 and 6.
Rewrite the middle term: 2x^2 + 6x + x + 3.
Group the terms: (2x^2 + 6x) + (x + 3).
Find the common factors: 2x(x + 3) + 1(x + 3).
Simplify: (2x + 1)(x + 3).