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If x^2-1 is a factor of a x^4+b x^3+c ...

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

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. Without actual division, prove that 2x^4-5x^3+2x^2-x+2 is exactly divi...

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

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  3. 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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  4. In each of the following two polynomials, find the value of a , if x...

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

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

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  8. 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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  9. Using factor theorem, factorize the following polynomial : x^3+2x^2...

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

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

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

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

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

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  16. Find the remainder when p(x)=4x^3-12 x^2+14 x-3 is divided by g(x)=x-1...

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  17. Find the remainder when p(x)=x^3-a x^2+6x-a is divided by (x-a)dot

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  18. Find the integral roots of the polynomial f(X) = x^3 + 6x^2 + 11x + 6

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  19. What must be subtracted from x^3-6x^2-15 x+80 so that the result is ex...

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  20. If x^3+a x^2-b x+10 is divisible by x^2-3x+2, find the values of a and...

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