Worksheets — Set 1

Algebra II · Rational expressions and functions

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

Warm-up

1. Factor completely: x² − 25 = ___ 2. Rewrite x² + 10x + 11 in square form: ___ 3. Interpret the structure of: 4(x + 1)² − 6

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 16 = ___ 2. Rewrite x² + 8x + 10 in square form: ___ 3. Interpret the structure of: 3(x + 1)² − 5 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 5x + ___ 6. Simplify: √(x² + 2x + 1) for x ≥ 0 = ___ 7. Factor completely: x² − 49 = ___ 8. Rewrite x² + 14x + 13 in square form: ___

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More written practice

1. Interpret the structure of: 6(x + 1)² − 8 2. Complete the square for x² + 8x + ___ 3. Simplify: √(x² + 8x + 16) for x ≥ 0 = ___ 4. Factor completely: x² − 100 = ___ 5. Rewrite x² + 20x + 16 in square form: ___ 6. Interpret the structure of: 9(x + 1)² − 11

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Patterns and rules

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._

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Parent tip: Look for common factors and special patterns