The AC Method is a powerful technique for factoring quadratic expressions of the form ax squared plus bx plus c, where the leading coefficient a is not equal to 1. This method becomes especially useful when traditional factoring approaches become challenging. For example, consider the expression 2x squared plus 7x plus 3. When the leading coefficient is not 1, we need a systematic approach to find the correct factorization.
To use the AC method, we follow three key steps. First, identify the coefficients a, b, and c from the quadratic expression. In our example 2x squared plus 7x plus 3, we have a equals 2, b equals 7, and c equals 3. Second, calculate the AC product by multiplying a times c, which gives us 2 times 3 equals 6. Third, find two numbers that multiply to give AC and add to give B. For AC equals 6 and B equals 7, we need factors of 6 that add to 7. Testing the factors: 1 times 6 equals 6, and 1 plus 6 equals 7, which works perfectly. So our two numbers are 6 and 1.