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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` , remainders are `5` and `19` respectively. Determine the remainder when `f(x)` is divided by `x-3.`

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. Find the rational roots of the polynomial 2x^3+3x^2-11 x-6

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  2. If x=0 and x=-1 are the roots of the polynomial f(x)=2x^3-3x^2+a x+b ,...

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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. Using factor theorem, factorize the polynomial x^4+2x^3-13 x^2-14 x+24

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  5. Factorize : 2x^4+x^3-14 x^2-19 x-6

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

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  7. Factorize x^3+13 x^2+32 x+20 , if it is given that x+2 is its factor.

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  8. 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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  9. In each of the following two polynomials, find the value of a , if x...

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

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

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  12. If x-2 is a factor of each of the following two polynomials, find th...

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  13. 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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  14. Using factor theorem, factorize the following polynomial : x^3+2x^2...

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

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  16. 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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  17. Let R1 and R2 are the remainders when the polynomials x^3+2x^2-5a x-7 ...

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  18. The polynomials a x^3+3x^2-13 and 2x^3-5x+a are divided by x+2, if the...

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  19. If the polynomials a x^3+4x^2+3x-4 and x^3-4x+a leave the same remaind...

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  20. Find the remainder when f(x)=x^3-6x^2+2x-4 is divided by g(x)=3x-1.

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