University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

127

Pages:

3
Author:

Gerardo Fox

Factoring x² + bx + c Factoring - Two Ways x² + 6x + 8 Method 1: List factors of 8: 1 & 8, 2 & 4 Pick the pair that adds to 6: 2 and 4 (x + 2)(x + 4) Method 2 (Visual Representation): A diagram with "x²" at the top, "6x" in the middle, and "8" at the bottom. Lines connect "x²" to "2x" and "4x" (factors of 6x). Lines connect "2x" and "4x" to "8". This visually represents the factors: (x + 2)(x + 4) Things to Consider Factoring x² + bx + c When c Is Positive Algebra: x² + bx + c = (x + p)(x + q) when p + q = b and pq = c. When c is positive, p and q have the same sign as b. Examples: x² + 6x + 5 = (x + 1)(x + 5) (both +) x² - 6x + 5 = (x - 1)(x - 5) (both -) Factoring x² + bx + c When c Is Negative Algebra: x² + bx + c = (x + p)(x + q) when p + q = b and pq = c. When c is negative, p and q have different signs. Example: x² - 4x - 5 = (x + 1)(x - 5) (each +/- ) Problems and Solutions c² + 8c + 7 (c + 1)(c + 7) a² + 16a + 64 (a + 8)(a + 8) or (a + 8)² x² + 11x + 18 (x + 2)(x + 9) d² + 6d + 8 (d + 2)(d + 4) s² + 11s + 10 (s + 1)(s + 10) u² + 10u + 9 (u + 1)(u + 9) b² + 3b - 54 (b + 9)(b - 6) y² + y - 2 (y + 1)(y - 2) u² + 3u - 18 (u - 3)(u + 6) z² - z - 56 (z - 8)(z + 7) h² + 2h - 24 (h - 4)(h + 6) f² - 3f - 40 (f + 5)(f - 8)