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Use factor theorem to verify that x+a is...

Use factor theorem to verify that `x+a` is a factor of `x^n+a^n` for any odd positive integer.

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To verify that \(x + a\) is a factor of \(x^n + a^n\) for any odd positive integer \(n\) using the factor theorem, we can follow these steps: ### Step 1: Define the Polynomial We start with the polynomial: \[ f(x) = x^n + a^n \] ...
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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. 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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  2. Using factor theorem, factorize the following polynomial : x^3+2x^2...

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

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

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

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

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

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

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

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

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  13. 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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  14. What must be subtracted from 4x^4-2x^3-6x^2+x-5 so that the result is...

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  15. The polynomials a x^3+3x^2-3 and 2x^3-5x+a when divided by (x-4) leave...

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  16. If the polynomials 2x^3+a x^2+3x-5 and x^3+x^2-4x+a leave the same rem...

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

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  18. Factorize 9z^3-27 z^2-100 z+300 , if it is given that (3z+10) is a fac...

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  19. Using factor theorem, factorize each of the following polynomials : ...

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  20. Using factor theorem, factorize each of the following polynomials :...

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