Breaking down a trinomial like ax2 + bx + c into two binomials is a core math skill. When the leading coefficient is not 1, you need a reliable method to find the right factor pairs. You will learn two widely used approaches: the AC method and trial and error.
The AC method gives you a clear, repeatable way to factor an expression with a leading coefficient other than 1. To factor ax2 + bx + c, follow these steps:
Example: Factor 2x2 + 7x + 3. AC = 2 × 3 = 6. Two numbers with product 6 and sum 7 are 1 and 6. Rewrite: 2x2 + x + 6x + 3. Group: x(2x + 1) + 3(2x + 1) = (x + 3)(2x + 1).
Trial and error is another way to find factor pairs for trinomials. You write two binomials of the form (px + q)(rx + s) and test pairs of numbers until the product matches the original trinomial. Use FOIL (First, Outer, Inner, Last) to check each attempt. A negative factor in the original trinomial is a sign to include a negative number in one of the binomials. When c is negative, the factors have opposite signs.
| Question | Answer |
|---|---|
| Form Name | Algebra Ax2 Factoring |
| Form Length | 1 pages |
| Fillable? | No |
| Fillable fields | 0 |
| Avg. time to fill out | 15 sec |
| Other names | factoring ax 2 bx c worksheet, factoring ax2 bx c answer key, factoring trinomials ax2 bx c worksheet, factoring trinomials of the form ax2 bx c answer key |
