Worksheets — Set 17

Algebra II · Quadratic and polynomial functions

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

Warm-up

1. Expand: (x + 2)(x + 3) = ___ 2. Add: (21x² + 2x + 1) + (18x² − x + 4) = ___ 3. Factor: x² + 23x + 24 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

1. Expand: (x + 4)(x + 4) = ___ 2. Add: (20x² + 2x + 1) + (17x² − x + 4) = ___ 3. Factor: x² + 22x + 23 = (x + ___)(x + ___) 4. Divide: (x² − 21) ÷ (x − 4). Quotient? ___ 5. If p(19) = 0, is (x − 19) a factor? ___ 6. Simplify: (19x³)(−2x²) = ___ 7. Expand: (x + 4)(x + 3) = ___ 8. Add: (23x² + 2x + 1) + (20x² − x + 4) = ___

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More written practice

1. Factor: x² + 25x + 26 = (x + ___)(x + ___) 2. Divide: (x² − 24) ÷ (x − 4). Quotient? ___ 3. If p(22) = 0, is (x − 22) a factor? ___ 4. Simplify: (22x³)(−1x²) = ___ 5. Add: (26x² + 2x + 1) + (23x² − x + 4) = ___ 6. Factor: x² + 28x + 29 = (x + ___)(x + ___)

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Patterns and rules

1. Expand: (x + 3)(x + 3) = ___ 2. Add: (37x² + 2x + 1) + (34x² − x + 4) = ___ 3. Factor: x² + 39x + 40 = (x + ___)(x + ___)

_See printable PDF for diagram._

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Stretch

1. Expand: (x + 2)(x + 3) = ___ 2. Add: (45x² + 2x + 1) + (42x² − x + 4) = ___

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Parent tip: Combine like terms before operating