Worksheets — Set 19

Algebra II · Rational expressions and functions

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

Warm-up

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._

Written practice

1. Factor completely: x² − 484 = ___ 2. Rewrite x² + 44x + 28 in square form: ___ 3. Interpret the structure of: 21(x + 1)² − 23 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 23x + ___ 6. Simplify: √(x² + 38x + 361) for x ≥ 0 = ___ 7. Factor completely: x² − 625 = ___ 8. Rewrite x² + 50x + 31 in square form: ___

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More written practice

1. Interpret the structure of: 24(x + 1)² − 26 2. Complete the square for x² + 26x + ___ 3. Simplify: √(x² + 44x + 484) for x ≥ 0 = ___ 4. Factor completely: x² − 784 = ___ 5. Rewrite x² + 56x + 34 in square form: ___ 6. Interpret the structure of: 27(x + 1)² − 29

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Patterns and rules

1. Factor completely: x² − 1521 = ___ 2. Rewrite x² + 78x + 45 in square form: ___ 3. Interpret the structure of: 38(x + 1)² − 40

_See printable PDF for diagram._

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Stretch

1. Factor completely: x² − 2209 = ___ 2. Rewrite x² + 94x + 53 in square form: ___

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Parent tip: Look for common factors and special patterns