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

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. For what values of a is 2x^3+a x^2+11 x+a+3 exactly divisible by (2x-1...

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  2. If a x^3+b x^2+x-6 has x+2 as a factor and leaves a remainder 4 when d...

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

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  4. If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=...

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  5. Without actual division, prove that 2x^4-5x^3+2x^2-x+2 is exactly divi...

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  6. Without actual division, prove that x^4+2x^3-2x^2+2x-3 is exactly divi...

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  7. In each of the following polynomials, find the value of a if x+a is...

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  8. In each of the following polynomials, find the value of a if x+a is...

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  9. Use factor theorem to verify that x+a is a factor of x^n+a^n for any o...

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  10. If f(x)=x^4-2x^3+3x^2-a x+b is a polynomial such that when it is divid...

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  11. What must be subtracted from 4x^4-2x^3-6x^2+x-5 so that the result is...

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  12. What must be added to x^4+2x^3-2x^2+x-1 so that the result is exactly ...

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  13. Use factor theorem to find whether polynomial g(x) is a factor of poly...

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  14. f(x)=3x^4+17 x^3+9x^2-7x-10 ;g(x)=x+5 find the remainder when f(x) is ...

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  15. check whether g(x) is a factor of f(x) or not f(x)=x^5+3x^4−x^3−3x^2+...

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  16. f(x)=x^3-6x^2-19 x+84 ,\ g(x)=x-7 find the value of f(x)-g(x).

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  17. f(x)=3x^3+x^2-20 x+12 ,\ g(x)=3x-2 find the remainder when f(x) is div...

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  18. Use factor theorem to find whether polynomial g(x) is a factor of poly...

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  19. f(x)=x^3-6x^2+11 x-6,\ g(x)=x^2-3x+2 find the remainder when f(x) is d...

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  20. Show that (x-2),(x+3) and (x-4) are factors of x^3-3x^2-10x+24.

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