Q:

1. Factor each of the following completely. Look carefully at the structure of each quadratic function and consider the best way to factor. Is there a GCF? Is it an example of a special case? SHOW YOUR WORK

Accepted Solution

A:
Answer: 1) (x - 7)(x - 8)                2) 2x(2x-7)(x + 2)                3) (4x + 7)²                4) (9ab² - c³)(9ab² + c³)Step-by-step explanation:1) x² - 15x + 56  → use standard form for factoring                     ∧                 -7 + -8 = -15   (x - 7) (x - 8)************************************2) 4x³ - 6x² - 28x      → factor out the GCF (2x)2x(2x² - 3x - 14)         → factor using grouping2x[2x² + 4x    - 7x - 14]     2x[ 2x(x + 2)   -7(x + 2)]2x(2x - 7)(x + 2)*************************************3) 16x² + 56x + 49     → this is the sum of squares√(16x²) = 4x      √(49) = 7               (4x + 7)²******************************************************4) 81a²b⁴ - c⁶          → this is the difference of squares√(81a²b⁴) = 9ab²       √(c⁶) = c³        (9ab² - c³)(9ab² + c³)