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Find the remainder when x^3+3x^2+3x+1 is...

Find the remainder when `x^3+3x^2+3x+1` is divided by (i) `x+1` (ii) `x-1/2` (iii) `x` (iv) `x+pi` (v) `5+2x`

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RD SHARMA ENGLISH-FACTORIZATION OF POLYNOMIAL-All Questions
  1. The polynomials a x^3+3x^2-3 and 2x^3-5x+a when divided by (x-4) leave...

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  2. If the polynomials a x^3+3x^2-13 and 2x^3-5x+a , when divided by (x-2)...

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  3. Find the remainder when x^3+3x^2+3x+1 is divided by (i) x+1 (ii) x...

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  4. Find the remainder when x^3+3x^2+3x+1 is divided by (i) x+1 (ii) x...

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  5. Show that (x-3) is a factor of the polynomial x^3-3x^2+4x-12

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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 and 2x-3 are factors of 2x^3-9x^2+x+12

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  8. Without actual division prove that 2x^4- 6x^3 +3x^2+3x-2 is exactly di...

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

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  10. Find the value of k , if x+3 is a factor of 3x^2+k x+6.

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  11. Determine the value of a for which the polynomial 2x^4-a x^3+4x^2+2x+1...

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  12. Find the value of a and b so that the polynomial x^3-a x^2-13 x+b has ...

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  13. Find the values of a and b so that the polynomial x^3+10 x^2+a x+b is ...

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  14. For what values of a is 2x^3+a x^2+11 x+a+3 exactly divisible by (2x-1...

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  15. If a x^3+b x^2+x-6 has x+2 as a factor and leaves a remainder 4 when d...

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  16. If both x-2 and x-1/2 are factors of p x^2+5x+r , show that p=rdot

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  17. If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=...

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  18. Without actual division, prove that 2x^4-5x^3+2x^2-x+2 is exactly divi...

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  19. Without actual division, prove that x^4+2x^3-2x^2+2x-3 is exactly divi...

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  20. In each of the following polynomials, find the value of a if x+a is...

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