Maths Uncategorized

GCD of Polynomials

August 6, 2023
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Questions

  1. Find the GCD of ( x^3 + x^2 – 4x – 6 ) and ( x^2 + 2x – 3 ).
  2. Determine the GCD of ( x^4 – 16 ) and ( x^2 – 4 ).
  3. Find the GCD of ( x^5 – x^3 + x^2 – x ) and ( x^4 – x^2 + x ).
  4. Determine the GCD of ( x^4 + 2x^3 + x^2 ) and ( x^3 + x^2 + x ).
  5. Find the GCD of ( 2x^4 – 6x^3 + 4x^2 ) and ( 2x^3 – 3x^2 + x ).
  6. Determine the GCD of ( 3x^4 – x^2 ) and ( 3x^2 + 6x ).
  7. Find the GCD of ( x^6 + 2x^4 – x^2 ) and ( x^4 + x^2 – 1 ).
  8. Determine the GCD of ( x^3 – 3x^2 + 2x ) and ( x^4 – 4x^3 + 6x^2 ).
  9. Find the GCD of ( 2x^5 – 3x^3 + x ) and ( 2x^4 – 3x^2 + 1 ).
  10. Determine the GCD of ( x^5 – x^3 + 4x^2 – 4 ) and ( x^4 – x^3 + 3x^2 – 3 ).
  11. Find the GCD of ( x^6 – x^5 + 5x^4 – 10x^3 ) and ( x^4 – 10x^2 + 9 ).
  12. Determine the GCD of ( 3x^4 – 2x^3 + x^2 ) and ( 3x^3 – x^2 + 2 ).
  13. Find the GCD of ( x^6 + x^5 – 5x^4 ) and ( x^5 – x^4 + x^3 ).
  14. Determine the GCD of ( 4x^4 – 6x^2 + 2 ) and ( 2x^4 – 3x^2 + 1 ).
  15. Find the GCD of ( x^4 + 4x^3 – x^2 – 4x ) and ( x^3 + 3x^2 – x – 3 ).
  16. Determine the GCD of ( x^7 – x^5 + x^4 – x^3 ) and ( x^6 – x^4 + x^3 – x^2 ).
  17. Find the GCD of ( 5x^4 – 10x^3 + 5x^2 ) and ( 5x^3 – 5x^2 + x ).
  18. Determine the GCD of ( x^5 + 2x^4 – x^3 – 2x^2 ) and ( x^4 + x^3 – x^2 – x ).
  19. Find the GCD of ( 3x^5 – 2x^4 + 6x^3 – 4x^2 ) and ( 3x^4 – 2x^3 + 3x^2 – 2x ).
  20. Determine the GCD of ( x^8 – x^6 + x^5 – x^3 ) and ( x^7 – x^5 + x^4 – x^2 ).

Answers

  1. ( x – 3 )
  2. ( x^2 – 4 )
  3. ( x^2 – 1 )
  4. ( x^2 + x )
  5. ( 2x^2 – x )
  6. ( 3x^2 )
  7. ( x^2 – 1 )
  8. ( x^2 – x )
  9. ( 2x^3 – x )
  10. ( x^3 – x^2 + 1 )
  11. ( x^2 – 1 )
  12. ( x^2 – 1 )
  13. ( x^4 )
  14. ( 2x^2 – 1 )
  15. ( x^3 + x^2 )
  16. ( x^5 – x^3 )
  17. ( 5x^2 )
  18. ( x^3 – x )
  19. ( 3x^3 – x )
  20. ( x^6 – x^4 )