Chapter 8 Test #2 (Solve Quadratics by Factoring)
Give a detailed summary of the process of solving a quadratic equation by factoring.
1. Get EQUATION set EQUAL TO 0. 2. FACTOR the quadratic expression, using common factoring patterns (GCF, 1x² Trinomial, Difference of Squares, or Perfect Square Trinomial) 3. Apply ZPP (Zero Product Property) -- set each factor equal to 0, then solve for the two solutions. 4. CHECK solutions by plugging into original equation to verify they make the equation TRUE!
Solve by factoring. Name the factoring pattern used. x² - 50 = -5x
Pattern: 1x² Trinomial Solutions: x = -10, x = 5 x² - 50 = -5x x² + 5x - 50 = 0 (x + 10)(x - 5) = 0 x + 10 = 0, x - 5 = 0
Solve by factoring. Name the factoring pattern used. x² - 8x = -15
Pattern: 1x² Trinomial Solutions: x = 3, x = 5 x² - 8x = -15 x² - 8x + 15 = 0 (x - 3)(x - 5) = 0 x - 3 = 0, x - 5 = 0
Solve by factoring. Name the factoring pattern used. x² - 5x - 6 = 0
Pattern: 1x² Trinomial Solutions: x = 6, x = -1 x² - 5x - 6 = 0 (x - 6)(x + 1) = 0 x - 6 = 0, x + 1 = 0
Solve by factoring. Name the factoring pattern used. x² - 3x - 28 = 0
Pattern: 1x² Trinomial Solutions: x = 7, x = -4 x² - 3x - 28 = 0 (x - 7)(x + 4) = 0 x - 7 = 0, x + 4 = 0
Solve by factoring. Name the factoring pattern used. 9x² = 25
Pattern: Difference of Squares Solutions: x = -5/3, x = 5/3 9x² = 25 9x² - 25 = 0 (3x + 5)(3x - 5) = 0
Solve by factoring. Name the factoring pattern used. 25x² = 64
Pattern: Difference of Squares Solutions: x = -8/5, x = 8/5 25x² = 64 25x² - 64 = 0 (5x + 8)(5x - 8) = 0 5x + 8 = 0, 5x - 8 = 0
Solve by factoring. Name the factoring pattern used. 12x = 6x²
Pattern: GCF Solutions: x = 0, x = -2 -12x = 6x² 0 = 6x² + 12x 0 = 6x(x + 2) 6x = 0, x + 2 = 0
Solve by factoring. Name the factoring pattern used. 3x² - 6x = 0
Pattern: Greatest Common Factor Solutions: x = 0, x = 2 3x² - 6x = 0 x(3x - 6) = 0 x = 0, 3x - 6 = 0
Solve by factoring. Name the factoring pattern used. 49a² - 28a + 4 = 0
Pattern: Perfect Square Trinomial Solutions:* a = 4/7 (double root) 49a² - 28a + 4 = 0 (7a - 4)(7a - 4) = 0 7a - 4 = 0
Solve by factoring. Name the factoring pattern used. 9y² - 12y = -4
Pattern: Perfect Square Trinomial Solutions:* y = 2/3 ("double root") 9y² - 12y = -4 9y² - 12y + 4 = 0 (3y - 2)(3y - 2) = 0 3y - 2 = 0