Factoring Advanced: ax² + bx + c and Grouping

When a neq 1, factoring is harder. Use the AC method: 1. Multiply a times c 2. Find two numbers that multiply to ac and add to b 3. Rewrite the middle term using those two numbers 4. Factor by grouping

Example: Factor 2x^2 + 7x + 3

For small coefficients, guessing and checking can be faster: ax^2 + bx + c = (_ x + _)(_ x + _) The first blanks must multiply to a, the last blanks to c. Try combinations until the cross-products add to b. Example: 6x^2 + 11x + 4 - 6 = 6 times 1 or 3 times 2 - 4 = 4 times 1 or 2 times 2 - Try (3x + 4)(2x + 1): 3x cdot 1 + 4 cdot 2x = 3x + 8x = 11x ✓