Worksheets — Set 3

Pre-calculus · Sequences, series, and limits (intro)

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

Warm-up

1. Factor completely: x² − 49 = ___ 2. Rewrite x² + 14x + 13 in square form: ___ 3. Interpret the structure of: 6(x + 1)² − 8

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 36 = ___ 2. Rewrite x² + 12x + 12 in square form: ___ 3. Interpret the structure of: 5(x + 1)² − 7 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 7x + ___ 6. Simplify: √(x² + 6x + 9) for x ≥ 0 = ___ 7. Factor completely: x² − 81 = ___ 8. Rewrite x² + 18x + 15 in square form: ___

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More written practice

1. Interpret the structure of: 8(x + 1)² − 10 2. Complete the square for x² + 10x + ___ 3. Simplify: √(x² + 12x + 36) for x ≥ 0 = ___ 4. Factor completely: x² − 144 = ___ 5. Rewrite x² + 24x + 18 in square form: ___ 6. Interpret the structure of: 11(x + 1)² − 13

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Patterns and rules

1. Factor completely: x² − 529 = ___ 2. Rewrite x² + 46x + 29 in square form: ___ 3. Interpret the structure of: 22(x + 1)² − 24

_See printable PDF for diagram._

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Parent tip: Look for common factors and special patterns