Worksheets — Set 20

Algebra II · Rational expressions and functions

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

Warm-up

1. Factor completely: x² − 576 = ___ 2. Rewrite x² + 48x + 30 in square form: ___ 3. Interpret the structure of: 23(x + 1)² − 25

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 529 = ___ 2. Rewrite x² + 46x + 29 in square form: ___ 3. Interpret the structure of: 22(x + 1)² − 24 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 24x + ___ 6. Simplify: √(x² + 40x + 400) for x ≥ 0 = ___ 7. Factor completely: x² − 676 = ___ 8. Rewrite x² + 52x + 32 in square form: ___

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More written practice

1. Interpret the structure of: 25(x + 1)² − 27 2. Complete the square for x² + 27x + ___ 3. Simplify: √(x² + 46x + 529) for x ≥ 0 = ___ 4. Factor completely: x² − 841 = ___ 5. Rewrite x² + 58x + 35 in square form: ___ 6. Interpret the structure of: 28(x + 1)² − 30

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Patterns and rules

1. Factor completely: x² − 1600 = ___ 2. Rewrite x² + 80x + 46 in square form: ___ 3. Interpret the structure of: 39(x + 1)² − 41

_See printable PDF for diagram._

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Stretch

1. Factor completely: x² − 2304 = ___ 2. Rewrite x² + 96x + 54 in square form: ___

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Parent tip: Look for common factors and special patterns