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If the polynomials 2x^3+a x^2+3x-5 and x...

If the polynomials `2x^3+a x^2+3x-5` and `x^3+x^2-4x+a` leave the same remainder when divided by `x-2,` find the value of `adot`

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To solve the problem, we need to find the value of \( a \) such that the polynomials \( f(x) = 2x^3 + ax^2 + 3x - 5 \) and \( g(x) = x^3 + x^2 - 4x + a \) leave the same remainder when divided by \( x - 2 \). ### Step-by-Step Solution: 1. **Identify the Remainder**: When a polynomial \( p(x) \) is divided by \( x - c \), the remainder is given by \( p(c) \). Here, we will evaluate both polynomials at \( x = 2 \). 2. **Evaluate \( f(2) \)**: ...
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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. What must be subtracted from 4x^4-2x^3-6x^2+x-5 so that the result is...

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

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

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

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

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

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

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

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

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

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  12. Which of the following expressions are polynomials in one variable ...

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  13. Which of the following expressions are polynomials in one variable ...

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  14. Which of the following expressions are polynomials in one variable ...

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  15. Write the coefficient of x^2 in each of the following: (i) 17-2x+7...

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  16. Write the coefficient of x^2 in each of the following: (i) pi/6x^2...

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  17. Write the degrees of each of the following polynomials: (i)7x^3+4x^2...

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  18. Write the degrees of each of the following polynomials: 7x^3+4x^2-...

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  19. Classify the following polynomials as linear, quadratic, cubic and b...

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  20. Classify the following polynomials as linear, quadratic, cubic and b...

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