Worksheets — Set 10

Algebra I · Honors · Rational expressions (intro)

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

Warm-up

1. Factor completely: x² − 196 = ___ 2. Rewrite x² + 28x + 20 in square form: ___ 3. Interpret the structure of: 13(x + 1)² − 15

_See printable PDF for diagram._

Written practice

1. Factor completely: x² − 169 = ___ 2. Rewrite x² + 26x + 19 in square form: ___ 3. Interpret the structure of: 12(x + 1)² − 14 4. Which form reveals zeros? (A) standard (B) factored — letter: ___ 5. Complete the square for x² + 14x + ___ 6. Simplify: √(x² + 20x + 100) for x ≥ 0 = ___ 7. Factor completely: x² − 256 = ___ 8. Rewrite x² + 32x + 22 in square form: ___

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More written practice

1. Interpret the structure of: 15(x + 1)² − 17 2. Complete the square for x² + 17x + ___ 3. Simplify: √(x² + 26x + 169) for x ≥ 0 = ___ 4. Factor completely: x² − 361 = ___ 5. Rewrite x² + 38x + 25 in square form: ___ 6. Interpret the structure of: 18(x + 1)² − 20

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Patterns and rules

1. Factor completely: x² − 900 = ___ 2. Rewrite x² + 60x + 36 in square form: ___ 3. Interpret the structure of: 29(x + 1)² − 31

_See printable PDF for diagram._

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Parent tip: Look for common factors and special patterns