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Factoring Polynomials Name ____________________________ Directions: Factor each expression completely and find the answer in the answer chart. Use the corresponding letters to decode the message below. Be careful! There are more answers than questions. Be sure to show all work! ___ ___ ___ ___ ___ ___ ___ ___ ___ 1 3 12 5 7 8 14 10 ___ ___ ___ ___ ___ ___ ___ 11 2 2 17 ___ ___ 7 1 14 10 4 ___ ___ ___ ___ ___ ___ 14 17 16 ___ ___ ___ ___ 6 9 ___ ___ ___ 5 6 2 3 12 14 13 ___ ___ ___ 13 3 17 ___ ___ ___ ___ ___ ___ ! 17 3 15 2 8 1. Factor: x 2 − 2 x − 15 2. Factor: 16 x 2 − 81 3. Factor: 24 x 3 y − 54 xy 4. Factor: 4 x 6 − 64 x 2 5. Factor: x8 − 1 6. Factor: x 4 y 2 − 4 x 3 y 2 − 12 x 2 y 2 7. Factor: x 2 a + 4 x a − 32 8. Factor: 12 x −3 − 3 x −5 All Rights Reserved © MathBits.com 16 17 2 9. Factor: − x 2 − 9 x + 22 10. Factor x3 − 5 x 2 + 2 x − 10 by grouping 11. Factor: x8 − y 4 12. Factor: 8 x 2 − 10 x − 3 13. Factor: −3x 4 + 30 x3 − 75 x 2 14. Factor: 4 x( x + 1) − 7( x + 1) 2 15. Factor: 5 x 5 − 10 x 4 + 25 x 3 − 50 x 2 16. Factor: x 6 a − 4 x 4 a 17. Factor: x3 − 8 Find your answers in the chart below: A D G J M P S V 6 xy (2 x − 3)(2 x + 3) x y ( x + 6)( x − 2) 2 2 x y ( x − 6)( x + 2) 2 2 4 x ( x − 16) 2 4 ( x + 1)( x − 1)( x − 5) ( x 2 − y )( x 2 + y )( x 4 + y 2 ) x 4 a ( x a − 2)( x a + 2) −5 3x (4 x − 1) 2 B E H K N Q T W −( x + 11)( x − 2) (4 x − 9)(4 x + 9) 4 x ( x + 4)( x − 2)( x + 2) 2 2 −3x ( x − 5) 2 2 ( x 2 + 2)( x − 5) ( x 4 − y 2 )( x 4 + y 2 ) ( x − 1)( x + 1)( x 2 + 1)( x 4 + 1) 6 xy (4 x − 9) 2 All Rights Reserved © MathBits.com C F I L O R U Y (4 x + 1)(2 x − 3) ( x − 5)( x + 3) −( x + 1)(3x + 7) ( x − 2)( x 2 + 2 x + 4) ( x a + 8)( x a − 4) 3x −5 (2 x − 1)(2 x + 1) (− x + 1)(3x + 7) 5 x 2 ( x 2 + 5)( x − 2)