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Prove that (x-1) is a factor of x^10-1 a...

Prove that (x-1) is a factor of `x^10-1` and `x^11-1`

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MODERN PUBLICATION-POLYNOMIALS-EXERCISE
  1. Find the value of k if (x+3) is a factor of 3x^3+kx+6

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  2. Prove that (x^3-3x^2-13x+15) is exactly divisible by x^2+2x-3

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  3. Prove that (x-1) is a factor of x^10-1 and x^11-1

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  4. Find the value of a and b so that the polynomial x^3-ax^2-13x+b has (x...

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  5. If ax^3+bx^2+x-6 has (x+2) as a factor and a remainder 4 when divided ...

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  6. If (x^2-1) is a factor of ax^4+bx^3+cx^2+dx+e if that a+c+e=b+d=0

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  7. If both (x+1) and (x-1) are factors of ax^3-2x+b, find the values of a...

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  8. find alpha and beta if (x+1) and (x+2) are factors x^3+3x^2-2alphax+be...

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  9. What must be added to 3x^3+x^2-22x+9 so the result is exactly divisibl...

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  10. What must be substracted from x^3-6x^2-15x+2 is so that the result is ...

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  11. Factorize the following expressions 18x^2y-24xyz

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  12. Factorize the following expressions 4(x+y)-6(x+y)^2

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  13. Factorize the following expressions 8(3a-2b)^2-10(3a-2b)

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  14. Factorize the following expressions ax-5b+ab-5x

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  15. Factorize the following expressions x^3-x^2+ax+x-a-1

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  16. Factorize the following expressions p^2+pq(q+1)+q^3

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  17. Factorize the following expressions a(a-2b-c)+2bc

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  18. Factorize the following expressions x^2-(a+b)x+ab

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  19. Factorize the following expressions x^2+1/x^2-2-3x+3/x

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  20. Factorize the following expressions 4a^2+12ab+9b^2-8a-12b

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