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Find `alpha\ a n d\ beta` , if `x+1\ a n d\ x+2` are factors of `x^3+3x^2-2alphax+beta`

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. Find the value of k if x-3 is a factor of k^2x^3-k x^2+3k x-k

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  2. Find the values of a and b, if x^2-4 is a factor of ax^4+2x^3-3x^2+bx-...

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  3. Find alpha\ a n d\ beta , if x+1\ a n d\ x+2 are factors of x^3+3x^2-2...

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  4. Find the values of p\ a n d\ q so that x^4+p x^3+2x^2-3x+q is divisibl...

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  5. Find the values of a\ a n d\ b so that (x+1)a n d\ (x-1) are factors o...

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  6. 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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  7. If (x+1) and (x-1) are factors of p(x)=ax^3+x^2-2x+b find the values o...

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  8. What must be added to x^3-3x^2-12 x+19 so that the result is exactl...

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

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  10. What must be added to 3x^3+x^2-22 x+9 so that the result is exactly di...

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  11. If x-2 is a factor of each of the following two polynomials, find th...

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

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

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  14. Show that (x-2) is a factor of the polynomial f(x)=2x^3-3x^2-17 x+30 a...

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  15. Using factor theorem, factorize the polynomial x^3-6x^2+11 x-6 .

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  16. Using factor theorem, factorize the polynomial x^4+x^3-7x^2-x+6

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  17. Using factor theorem, factorize the polynomial x^4-2x^3-13 x^2+14 x+2...

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  18. Factorize : 2x^4+x^3-14 x^2-19 x-6

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  19. Factorize x^3+13 x^2+32 x+20 , if it is given that x+2 is its factor.

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

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