2-3b Notes Algebra 2 Stailey

This video explains the Barry method for factoring quadratic trinomials, especially when the leading coefficient (the 'a' value) is not 1 and there's no common factor to pull out initially (0:12). The steps of the Barry method are: Check for a GCF: Always check if there's a greatest common factor in the original trinomial. If there is, factor it out first and keep it for the final answer (4:09, 9:40). Multiply 'a' and 'c': Multiply the leading coefficient ('a' value) by the constant term ('c' value) (0:30). Rewrite the trinomial as if the 'a' value was 1, using the new product as the constant term. The video emphasizes that this new expression is not equal to the original, but it's a step in the process (0:52). Factor the new trinomial: Factor this simpler quadratic trinomial into two binomials (1:33). Bring 'a' back: Reintroduce the original 'a' value in front of the 'x' in both binomials (2:28). Find and discard GCFs: Look for a GCF within each of the new binomials. If a GCF exists, factor it out and "throw it away" (3:02, 3:31). Final factored form: The remaining binomials form the correct factored form of the original trinomial (3:47). The video also touches on recognizing perfect square trinomials (12:41) as a special case, but notes that the Barry method still works if you don't spot the pattern (16:30).