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If f(x)=x^4-2x^3+3x^2-a x+b is a polynom...

If `f(x)=x^4-2x^3+3x^2-a x+b` is `a` polynomial such that when it is divided by `x-1` and `x+1,` the remainders are respectively `5` and `19.` Determine the remainder when `f(x)` is divided by `(x-2)dot`

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. In each of the following polynomials, find the value of a if x+a is...

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

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

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

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

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  7. 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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  8. 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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  9. 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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  10. 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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  11. Use factor theorem to find whether polynomial g(x) is a factor of poly...

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

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  14. Show that (x+4),\ (x-3)a n d\ (x-7) are factors of x^3-6x^2-19 x+84

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  15. For what value of a is (x-5) a factor of x^3-3x^2+a x-10 ?

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  16. Find the value of a such that (x-4) is a factor of 5x^3-7x^2-a x-28

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  17. Find the value of a , if x+2 is a factor of 4x^4+2x^3-3x^2+8x+5a

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  18. Find the value of k if x-3 is a factor of k^2x^3-k x^2+3k x-k

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  19. Find the values of a and b, if x^2-4 is a factor of ax^4+2x^3-3x^2+bx-...

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  20. Find alpha\ a n d\ beta , if x+1\ a n d\ x+2 are factors of x^3+3x^2-2...

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