Worksheets — Set 3

Pre-calculus · Honors · Symbolic manipulation at honors depth

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

Warm-up

1. Expand: (x + 3)(x + 3) = ___ 2. Add: (7x² + 2x + 1) + (4x² − x + 4) = ___ 3. Factor: x² + 9x + 10 = (x + ___)(x + ___)

_See printable PDF for diagram._

Written practice

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

___________________________ ___________________________ ___________________________ ___________________________

More written practice

1. Factor: x² + 11x + 12 = (x + ___)(x + ___) 2. Divide: (x² − 10) ÷ (x − 2). Quotient? ___ 3. If p(8) = 0, is (x − 8) a factor? ___ 4. Simplify: (8x³)(−1x²) = ___ 5. Add: (12x² + 2x + 1) + (9x² − x + 4) = ___ 6. Factor: x² + 14x + 15 = (x + ___)(x + ___)

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. Expand: (x + 4)(x + 3) = ___ 2. Add: (23x² + 2x + 1) + (20x² − x + 4) = ___ 3. Factor: x² + 25x + 26 = (x + ___)(x + ___)

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Combine like terms before operating