Worksheets — Set 16

Algebra II · Honors · Sequences, series, and summation

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. Factor completely: x² − 400 = ___ 2. Rewrite x² + 40x + 26 in square form: ___ 3. Interpret the structure of: 19(x + 1)² − 21

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 361 = ___ 2. Rewrite x² + 38x + 25 in square form: ___ 3. Interpret the structure of: 18(x + 1)² − 20 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 20x + ___ 6. Simplify: √(x² + 32x + 256) for x ≥ 0 = ___ 7. Factor completely: x² − 484 = ___ 8. Rewrite x² + 44x + 28 in square form: ___

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More written practice

1. Interpret the structure of: 21(x + 1)² − 23 2. Complete the square for x² + 23x + ___ 3. Simplify: √(x² + 38x + 361) for x ≥ 0 = ___ 4. Factor completely: x² − 625 = ___ 5. Rewrite x² + 50x + 31 in square form: ___ 6. Interpret the structure of: 24(x + 1)² − 26

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Patterns and rules

1. Factor completely: x² − 1296 = ___ 2. Rewrite x² + 72x + 42 in square form: ___ 3. Interpret the structure of: 35(x + 1)² − 37

_See printable PDF for diagram._

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Stretch

1. Factor completely: x² − 1936 = ___ 2. Rewrite x² + 88x + 50 in square form: ___

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Parent tip: Look for common factors and special patterns