Worksheets — Set 15

Pre-calculus · Polynomial and rational functions

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

Warm-up

1. Expand: (x + 3)(x + 3) = ___ 2. Add: (19x² + 2x + 1) + (16x² − x + 4) = ___ 3. Factor: x² + 21x + 22 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

1. Expand: (x + 2)(x + 4) = ___ 2. Add: (18x² + 2x + 1) + (15x² − x + 4) = ___ 3. Factor: x² + 20x + 21 = (x + ___)(x + ___) 4. Divide: (x² − 19) ÷ (x − 2). Quotient? ___ 5. If p(17) = 0, is (x − 17) a factor? ___ 6. Simplify: (17x³)(−2x²) = ___ 7. Expand: (x + 2)(x + 3) = ___ 8. Add: (21x² + 2x + 1) + (18x² − x + 4) = ___

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More written practice

1. Factor: x² + 23x + 24 = (x + ___)(x + ___) 2. Divide: (x² − 22) ÷ (x − 2). Quotient? ___ 3. If p(20) = 0, is (x − 20) a factor? ___ 4. Simplify: (20x³)(−1x²) = ___ 5. Add: (24x² + 2x + 1) + (21x² − x + 4) = ___ 6. Factor: x² + 26x + 27 = (x + ___)(x + ___)

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Patterns and rules

1. Expand: (x + 4)(x + 3) = ___ 2. Add: (35x² + 2x + 1) + (32x² − x + 4) = ___ 3. Factor: x² + 37x + 38 = (x + ___)(x + ___)

_See printable PDF for diagram._

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Parent tip: Combine like terms before operating