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If p(x) is a polynomial of degree nge1 a...

If p(x) is a polynomial of degree `nge1` and 'a' is any real number, then (i)(x-a) is a factor of p(x), if `p(a) = 0` (ii) and Its converse "if (x - a) is a factor of a polynomial p(x) then `p(a) = 0`." Let us see the simple proof of this theorem.

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VGS PUBLICATION-BRILLIANT-POLYNOMIAL AND FACTORIISATION-EXERCISE
  1. Find the remainder when p (x) = x ^(3) - 6x ^(2) + 14x -3 is divided b...

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  2. When a polynomial 2x ^(3) + 3x ^(2) + ax + b is divided by (x-2) leave...

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  3. If p(x) is a polynomial of degree nge1 and 'a' is any real number, the...

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  4. Examine whether x +2 is a factor of x ^(3) + 2x ^(2) + 3x +6

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  5. Find the value of K, if 2x-3 Is a factor of 2x^3-9x^2 +x+K.

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  6. Show that (x-1) is a factor of x ^(10) -1 and also of x ^(11) -1.

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  7. Show that (x-1) is a factor of x ^(n)-1.

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  8. Factorise 3x ^(2) + 11 x + 6

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  9. Fractorise the following (i) 6x ^(2) + 19 x + 15

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  10. Factors of 10 m ^(2) - 31m - 132

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  11. Factorise the following. 12x^2+11x+2

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  12. Verify whether 2x ^(4) - 6x ^(3) + 3x ^(2) + 3x -2 is divisible by x ^...

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  13. Factorise x ^(3) - 23 x ^(2) + 142 x -120

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  14. Determine which of the following polynomials has (x +1) as a factor. ...

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  15. Determine which of the following polynomials has (x +1) as a factor. ...

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  16. Determine which of the following polynomials has (x +1) as a factor. ...

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  17. Determine which of the following polynomials has (x +1) as a factor. ...

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  18. Use the Factor Theorem to determine whether g (x) is factor of f(x) in...

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  19. Use the Factor Theorem to determine whether g (x) is factor of f(x) in...

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  20. Use the Factor Theorem to determine whether g (x) is factor of f(x) in...

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