Worksheets — Set 8

Pre-calculus · Honors · Symbolic manipulation at honors depth

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

Warm-up

1. Expand: (x + 2)(x + 4) = ___ 2. Add: (12x² + 2x + 1) + (9x² − x + 4) = ___ 3. Factor: x² + 14x + 15 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

1. Expand: (x + 4)(x + 3) = ___ 2. Add: (11x² + 2x + 1) + (8x² − x + 4) = ___ 3. Factor: x² + 13x + 14 = (x + ___)(x + ___) 4. Divide: (x² − 12) ÷ (x − 4). Quotient? ___ 5. If p(10) = 0, is (x − 10) a factor? ___ 6. Simplify: (10x³)(−1x²) = ___ 7. Expand: (x + 4)(x + 4) = ___ 8. Add: (14x² + 2x + 1) + (11x² − x + 4) = ___

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More written practice

1. Factor: x² + 16x + 17 = (x + ___)(x + ___) 2. Divide: (x² − 15) ÷ (x − 4). Quotient? ___ 3. If p(13) = 0, is (x − 13) a factor? ___ 4. Simplify: (13x³)(−2x²) = ___ 5. Add: (17x² + 2x + 1) + (14x² − x + 4) = ___ 6. Factor: x² + 19x + 20 = (x + ___)(x + ___)

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Patterns and rules

1. Expand: (x + 3)(x + 4) = ___ 2. Add: (28x² + 2x + 1) + (25x² − x + 4) = ___ 3. Factor: x² + 30x + 31 = (x + ___)(x + ___)

_See printable PDF for diagram._

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Parent tip: Combine like terms before operating