Question

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

Answer 1

Answer: 1) (x - 7)(x - 8)

2) 2x(2x-7)(x + 2)

3) (4x + 7)²

4) (9ab² - c³)(9ab² + c³)

Explanation:

1) x² - 15x + 56 → use standard form for factoring

∧

-7 + -8 = -15

(x - 7) (x - 8)

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2) 4x³ - 6x² - 28x → factor out the GCF (2x)

2x(2x² - 3x - 14) → factor using grouping

2x[2x² + 4x - 7x - 14]

2x[ 2x(x + 2) -7(x + 2)]

2x(2x - 7)(x + 2)

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3) 16x² + 56x + 49 → this is the sum of squares

√(16x²) = 4x √(49) = 7

(4x + 7)²

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4) 81a²b⁴ - c⁶ → this is the difference of squares

√(81a²b⁴) = 9ab² √(c⁶) = c³

(9ab² - c³)(9ab² + c³)