Worksheets — Set 16
Pre-calculus · Polynomial and rational functions
Print and write your answers. Use diagrams to show thinking.
Warm-up
1. Expand: (x + 4)(x + 4) = ___ 2. Add: (20x² + 2x + 1) + (17x² − x + 4) = ___ 3. Factor: x² + 22x + 23 = (x + ___)(x + ___)
_See printable PDF for diagram._
Written practice
1. Expand: (x + 3)(x + 3) = ___ 2. Add: (19x² + 2x + 1) + (16x² − x + 4) = ___ 3. Factor: x² + 21x + 22 = (x + ___)(x + ___) 4. Divide: (x² − 20) ÷ (x − 3). Quotient? ___ 5. If p(18) = 0, is (x − 18) a factor? ___ 6. Simplify: (18x³)(−1x²) = ___ 7. Expand: (x + 3)(x + 4) = ___ 8. Add: (22x² + 2x + 1) + (19x² − x + 4) = ___
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More written practice
1. Factor: x² + 24x + 25 = (x + ___)(x + ___) 2. Divide: (x² − 23) ÷ (x − 3). Quotient? ___ 3. If p(21) = 0, is (x − 21) a factor? ___ 4. Simplify: (21x³)(−2x²) = ___ 5. Add: (25x² + 2x + 1) + (22x² − x + 4) = ___ 6. Factor: x² + 27x + 28 = (x + ___)(x + ___)
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Patterns and rules
1. Expand: (x + 2)(x + 4) = ___ 2. Add: (36x² + 2x + 1) + (33x² − x + 4) = ___ 3. Factor: x² + 38x + 39 = (x + ___)(x + ___)
_See printable PDF for diagram._
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Stretch
1. Expand: (x + 4)(x + 4) = ___ 2. Add: (44x² + 2x + 1) + (41x² − x + 4) = ___
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Parent tip: Combine like terms before operating