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If (x + p) be a common factor of both th...

If (x + p) be a common factor of both the polynomials `(x^(2)+ax+b)and(x^(2)+cx+d)`, then prove that `p=(b-d)/(a-c)`.

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CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.4
  1. If (x^(2)-2) be a factor of the polynomial (ax^(3)-bx^(2)-4), find the...

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  2. If m, n be natural numbers and (x^(2)-n) be a factor of the polynomial...

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  3. If (x - 1) and (x - 3) be two factors of the polynomial (x^(3)-3x^(2)+...

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  4. If x+a is a factor of x^2+px+q and x^2+mx+n, show that a= (n-q)/(m-p)...

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  5. If the polynomial (ax^(3)+bx^(2)-x+6) be divided by (x + 2), the remai...

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  6. If the polynomial (ax^(p)+bx^(q)-3) be divided by (x - a) and (x - b),...

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  7. Prove that the polynomial (x^(10)-y^(10)) is divisible by (x + y).

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  8. Prove that the polynomial (x^(99)-y^(99)) is not divisible by (x + y).

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  9. Prove that the polynomial (x^(100)-a^(100)) is divisible by (x + a), b...

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  10. Prove that the polynomial (x^(81)-2^(81)) is not divisible by (x + 2),...

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  11. Show that the polynomial (x^(70)+1) is not divisible by (x - 1)

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  12. Show that the polynomial (x^(71)+1) is not divisible by (x - 1), but i...

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  13. Prove that the polynomial (x^(-17)+1) is not divisible by (x - 1), but...

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  14. Prove that the polynomial (x^(-19)+y^(-19)) is not divisible by (x - y...

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  15. If (x + p) be a common factor of both the polynomials (x^(2)+ax+b)and(...

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  16. What is the condition that the polynomial {x^(2)+(p+q)x+r} is divisibl...

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  17. Determine the condition for which the polynomial x^(3)+(p-q)x+r is div...

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  18. Determine the relation between c and d if (x - 2) and (x-1/2) be the t...

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  19. If the ratio of the remainders when the polynomial (x^(2m)+1) is succe...

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  20. Determine the value of k if the ratio of the two remainders, obtained ...

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