Worksheets — Set 12

Algebra II · Rational expressions and functions

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

Warm-up

1. Factor completely: x² − 256 = ___ 2. Rewrite x² + 32x + 22 in square form: ___ 3. Interpret the structure of: 15(x + 1)² − 17

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 225 = ___ 2. Rewrite x² + 30x + 21 in square form: ___ 3. Interpret the structure of: 14(x + 1)² − 16 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 16x + ___ 6. Simplify: √(x² + 24x + 144) for x ≥ 0 = ___ 7. Factor completely: x² − 324 = ___ 8. Rewrite x² + 36x + 24 in square form: ___

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More written practice

1. Interpret the structure of: 17(x + 1)² − 19 2. Complete the square for x² + 19x + ___ 3. Simplify: √(x² + 30x + 225) for x ≥ 0 = ___ 4. Factor completely: x² − 441 = ___ 5. Rewrite x² + 42x + 27 in square form: ___ 6. Interpret the structure of: 20(x + 1)² − 22

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Patterns and rules

1. Factor completely: x² − 1024 = ___ 2. Rewrite x² + 64x + 38 in square form: ___ 3. Interpret the structure of: 31(x + 1)² − 33

_See printable PDF for diagram._

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Parent tip: Look for common factors and special patterns