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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. If x-2 is a factor of x^2+3a x-2a, then a= (a) 2 (b) -2 (c) 1 (...

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  2. If x^3+6x^2+4x+k , is exactly divisible by (x+2), then the value of k ...

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  3. If x-a is a factor of x^3-3x^2a+2a^2x+b , then the value of b is (a) ...

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  4. If x^(140)+2x^(151)+k is divisible by x+1 , then the value of k is=? ...

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  5. If x+2 and x-1 are the factors of x^3+10 x^2+m x+n, then the values of...

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  6. Let f(x) be a polynomial such that f(-1/2)=0, then a factor of f(x) ...

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  7. When x^3-2x^2+a x-b is divided by x^2-2x-3, the remainder is x-6. The ...

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  8. One factor of x^4+x^2-20 is x^2+5. The other factor is x^2-4\ (b) ...

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  9. If (x-1) is a factor of polynomial f(x) but not of g(x) , then it mu...

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  10. (x+1) is a factor of x^n+1 only if

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  11. If x+2\ is a factor of x^2+m x+14 , then m=

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  12. If x-3 is a factor of x^2-a x-15 , then a= (a) -2 (b) 5 (c) -5 ...

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  13. If x^2+x+1 is a factor of the polynomial 3x^3+8x^2+8x+3+5k , then th...

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  14. If (3x-1)^7=a7x^7+a6x^6+a5x^5+....+a1x+a0 then the value of a7 + a6. ....

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  15. If x^(51)+51 is divided by x+1 , the remainder is (a)0 (b) 1 (c) ...

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  16. If x+1 is a factor of the polynomial 2x^2+k x , then k= (a) -2 (...

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  17. If x+a is a factor of x^4-a^2x^2+3x-6a , then a=

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  18. Find the value of k, if x-1 is a factor of 4x^3+3x^2-4x+k .

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

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  20. 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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