Worksheets — Set 17

Algebra II · Radical expressions and equations

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

Warm-up

1. Factor completely: x² − 441 = ___ 2. Rewrite x² + 42x + 27 in square form: ___ 3. Interpret the structure of: 20(x + 1)² − 22

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 400 = ___ 2. Rewrite x² + 40x + 26 in square form: ___ 3. Interpret the structure of: 19(x + 1)² − 21 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 21x + ___ 6. Simplify: √(x² + 34x + 289) for x ≥ 0 = ___ 7. Factor completely: x² − 529 = ___ 8. Rewrite x² + 46x + 29 in square form: ___

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More written practice

1. Interpret the structure of: 22(x + 1)² − 24 2. Complete the square for x² + 24x + ___ 3. Simplify: √(x² + 40x + 400) for x ≥ 0 = ___ 4. Factor completely: x² − 676 = ___ 5. Rewrite x² + 52x + 32 in square form: ___ 6. Interpret the structure of: 25(x + 1)² − 27

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Patterns and rules

1. Factor completely: x² − 1369 = ___ 2. Rewrite x² + 74x + 43 in square form: ___ 3. Interpret the structure of: 36(x + 1)² − 38

_See printable PDF for diagram._

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Stretch

1. Factor completely: x² − 2025 = ___ 2. Rewrite x² + 90x + 51 in square form: ___

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Parent tip: Look for common factors and special patterns