Worksheets — Set 10

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 + 4) = ___ 2. Add: (14x² + 2x + 1) + (11x² − x + 4) = ___ 3. Factor: x² + 16x + 17 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

1. Expand: (x + 3)(x + 3) = ___ 2. Add: (13x² + 2x + 1) + (10x² − x + 4) = ___ 3. Factor: x² + 15x + 16 = (x + ___)(x + ___) 4. Divide: (x² − 14) ÷ (x − 3). Quotient? ___ 5. If p(12) = 0, is (x − 12) a factor? ___ 6. Simplify: (12x³)(−1x²) = ___ 7. Expand: (x + 3)(x + 4) = ___ 8. Add: (16x² + 2x + 1) + (13x² − x + 4) = ___

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More written practice

1. Factor: x² + 18x + 19 = (x + ___)(x + ___) 2. Divide: (x² − 17) ÷ (x − 3). Quotient? ___ 3. If p(15) = 0, is (x − 15) a factor? ___ 4. Simplify: (15x³)(−2x²) = ___ 5. Add: (19x² + 2x + 1) + (16x² − x + 4) = ___ 6. Factor: x² + 21x + 22 = (x + ___)(x + ___)

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Patterns and rules

1. Expand: (x + 2)(x + 4) = ___ 2. Add: (30x² + 2x + 1) + (27x² − x + 4) = ___ 3. Factor: x² + 32x + 33 = (x + ___)(x + ___)

_See printable PDF for diagram._

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Parent tip: Combine like terms before operating