Worksheets — Set 1

Pre-calculus · Honors · Symbolic manipulation at honors depth

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

Warm-up

1. Expand: (x + 4)(x + 3) = ___ 2. Add: (5x² + 2x + 1) + (2x² − x + 4) = ___ 3. Factor: x² + 7x + 8 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

1. Expand: (x + 3)(x + 4) = ___ 2. Add: (4x² + 2x + 1) + (1x² − x + 4) = ___ 3. Factor: x² + 6x + 7 = (x + ___)(x + ___) 4. Divide: (x² − 5) ÷ (x − 3). Quotient? ___ 5. If p(3) = 0, is (x − 3) a factor? ___ 6. Simplify: (3x³)(−2x²) = ___ 7. Expand: (x + 3)(x + 3) = ___ 8. Add: (7x² + 2x + 1) + (4x² − x + 4) = ___

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More written practice

1. Factor: x² + 9x + 10 = (x + ___)(x + ___) 2. Divide: (x² − 8) ÷ (x − 3). Quotient? ___ 3. If p(6) = 0, is (x − 6) a factor? ___ 4. Simplify: (6x³)(−1x²) = ___ 5. Add: (10x² + 2x + 1) + (7x² − x + 4) = ___ 6. Factor: x² + 12x + 13 = (x + ___)(x + ___)

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Patterns and rules

1. Expand: (x + 2)(x + 3) = ___ 2. Add: (21x² + 2x + 1) + (18x² − x + 4) = ___ 3. Factor: x² + 23x + 24 = (x + ___)(x + ___)

_See printable PDF for diagram._

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Parent tip: Combine like terms before operating