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Q.

What should be the correct arrangement of the given statements according to the working rule to divide a polynomial?

  1. If deg f(x) < deg g(x),  then f(x) = g(x)⋅0 + f(x), i.e., the quotient is 0 , and r(x)=f(x). 
  2. If deg f(x) ≥ deg g(x), then arrange the terms of both polynomials in standard form. Divide the first term of f(x) by the first term of g(x) to get the first term of q(x). Multiply the whole divisor, i.e., g(x),  by the first term of the quotient and then subtract it from the dividend to get the remainder. 
  3. If the deg r(x) ≥ deg g(x), treat this remainder as the new dividend and proceed as above. 
    Repeat till r(x) = 0 or deg r(x) < deg g(x) 
  4. If the final remainder is r(x) and the quotient is q(x), then f(x) = g(x)⋅q(x) + r(x), when either r(x) = 0 or deg r(x) < deg g(x).

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a

4, 2, 1, 3

b

1, 3, 2, 4

c

1, 2, 3, 4

d

4, 3, 1, 2

answer is A.

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Detailed Solution

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The correct arrangement of the given statements according to the working rule to divide a polynomial will be 1, 2, 3, 4.

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