1. Expand and Simplify
1.1. Special Products
1.1.1. Perfect Square Trinomial
1.1.1.1. (a + b)(a + b) = a^2 + 2ab + b^2
1.1.1.2. ( a- b)(a + b) = a^2 - 2ab +b^2
1.1.2. Difference of Squares
1.1.2.1. (a + b)(a - b) = (a^2 – b^2)
1.2. Multiplying Binomials (with other binomials)
1.2.1. (2a + 2)(4a + 4) = (2a x 4a) + (2a x 4) + (2 x 4a) + (2 x 4) = 8a^2 + 8a + 8a + 8 = 8a^2 + 16a + 8
2. Factoring
2.1. Binomials
2.1.1. Common Factors
2.1.1.1. 2b^2 - 4b GCF = 2b 2b^2/2b - 4b/2b = 2b (b - 2)
2.1.2. Difference of Squares
2.1.2.1. a^2 - b^2 = (a + b)(a - b)
2.2. Trinomials
2.2.1. a = 1
2.2.1.1. x^2 + 3x + 2 Product = 2 Sum = 3 (2, 1) x^2 + x + 2x + 2 (x^2 + x)/x = (2x + 2)/2 x(x + 1) + 2 (x +1) (x + 1) (x +2
2.2.2. a ≠ 1
2.2.2.1. 2x^2 + 5x + 2 NO GCF Product = 4 Sum = 5 (4, 1) 2x^2 + x + 4x + 2 (2x^2 + x)/x + (4x + 2)/2 x(2x + 1) + 2(2x +1) (x + 2)(2x + 1)
2.2.3. Perfect Square Trinomial
2.2.3.1. a^2 - 2ab + b^2 = (a - b)(a - b)
2.2.3.2. a^2 + 2ab + b^2 = (a + b)(a + b)
2.3. Four-term Polynomial
2.3.1. Grouping
2.3.1.1. 4b - 2b + 9c - 3c GCF 1 = 2b GCF 2 = 3c (4b/2b) - (2b/2b) + (6c/3c) - (3c/3c) = 2b(2 - 1) + 3c(2 - 1) = (2b + 3c) (2 - 1)
3. Graphing Quadratics with Factoring
3.1. Standard Form (y = ax^2 + bx + c)
3.1.1. Y-intercept (c-value of standard form)
3.2. Factored Form y = (x - r) (x -s)
3.2.1. X-intercepts/Zeroes/Roots
3.2.1.1. h (average of roots)
3.2.1.1.1. k (to find k, substitute it into the equation as x = 0)