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Without actually calculating the cubes, ...

Without actually calculating the cubes, find the value of:
`(1/2)^3+(1/3)^3-(5/6)^3`

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MODERN PUBLICATION-POLYNOMIALS-EXERCISE
  1. For some integer m, every even integer is of the form:

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  2. For some integer q, every odd integer is of the form

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  3. n^2-1 is divisible by 8, if n is

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  4. If the HCF of 65 and 117 is expressible in the form 65m-117, then the ...

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  5. The largest number which divides 70 and 125, leaving remainders 5 and ...

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  6. If two positive integers p and q can be expression as p=ab^2 and q=a^3...

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  7. The product of a non-zero rational and irrational number is

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  8. The least number that is divisible by all the numbers from 1 to 10 is

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  9. The decimal expansion of the rational number 14587/1250 will terminate...

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  10. Find the zeroes of the polynomial x^2-5x

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  11. Evaluate: (a-b)^3+(b-c)^3+(c-a)^3

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  12. Using Remainder theorem, find the remainder when 4x^3-12x^2+11x-5 is d...

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  13. Using factor theorem, prove that x-y is a factor of x(y^2-z^2)+y(z^2-x...

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  14. Show that p-1 is a factor of p^10-1 and also p^11-1

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  15. If x+2a is a factor of x^5-4a^2x^3+2x+2a+3 find a.

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  16. Without actually calculating the cubes, find the value of: (1/2)^3+(1/...

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  17. If both x-2 and x-1/2 are factors of px^2+5x+r, show that p=r.

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  18. Find the integral zeroes of the polynomial: p(x)=x^3+6x^2+11x+6

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  19. If x^2+1/x^2=79, evaluate x^3+1/x^3

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  20. Using factor theorem factorise p(x)=x^3-23x^2+142x-120

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