Worksheets — Set 11

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

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

Warm-up

1. Factor completely: x² − 225 = ___ 2. Rewrite x² + 30x + 21 in square form: ___ 3. Interpret the structure of: 14(x + 1)² − 16

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 196 = ___ 2. Rewrite x² + 28x + 20 in square form: ___ 3. Interpret the structure of: 13(x + 1)² − 15 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 15x + ___ 6. Simplify: √(x² + 22x + 121) for x ≥ 0 = ___ 7. Factor completely: x² − 289 = ___ 8. Rewrite x² + 34x + 23 in square form: ___

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More written practice

1. Interpret the structure of: 16(x + 1)² − 18 2. Complete the square for x² + 18x + ___ 3. Simplify: √(x² + 28x + 196) for x ≥ 0 = ___ 4. Factor completely: x² − 400 = ___ 5. Rewrite x² + 40x + 26 in square form: ___ 6. Interpret the structure of: 19(x + 1)² − 21

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Patterns and rules

1. Factor completely: x² − 961 = ___ 2. Rewrite x² + 62x + 37 in square form: ___ 3. Interpret the structure of: 30(x + 1)² − 32

_See printable PDF for diagram._

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Parent tip: Look for common factors and special patterns