GCD of Polynomials

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 )