Worksheets — Set 6

Pre-calculus · Polynomial and rational functions

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

Warm-up

1. Expand: (x + 3)(x + 4) = ___ 2. Add: (10x² + 2x + 1) + (7x² − x + 4) = ___ 3. Factor: x² + 12x + 13 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

1. Expand: (x + 2)(x + 3) = ___ 2. Add: (9x² + 2x + 1) + (6x² − x + 4) = ___ 3. Factor: x² + 11x + 12 = (x + ___)(x + ___) 4. Divide: (x² − 10) ÷ (x − 2). Quotient? ___ 5. If p(8) = 0, is (x − 8) a factor? ___ 6. Simplify: (8x³)(−1x²) = ___ 7. Expand: (x + 2)(x + 4) = ___ 8. Add: (12x² + 2x + 1) + (9x² − x + 4) = ___

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More written practice

1. Factor: x² + 14x + 15 = (x + ___)(x + ___) 2. Divide: (x² − 13) ÷ (x − 2). Quotient? ___ 3. If p(11) = 0, is (x − 11) a factor? ___ 4. Simplify: (11x³)(−2x²) = ___ 5. Add: (15x² + 2x + 1) + (12x² − x + 4) = ___ 6. Factor: x² + 17x + 18 = (x + ___)(x + ___)

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Patterns and rules

1. Expand: (x + 4)(x + 4) = ___ 2. Add: (26x² + 2x + 1) + (23x² − x + 4) = ___ 3. Factor: x² + 28x + 29 = (x + ___)(x + ___)

_See printable PDF for diagram._

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Parent tip: Combine like terms before operating