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Any polynomial p(x) of degree n ≥ 1 may be expressed as?
  1. p(x) = (x - r)q(x)k
  2. p(x) = (x - r)q(x) + k
  3. p(x) = (x - r)q(x) - k
  4. p(x) = (x + r)q(x) + k
  5. None of these
Explanation
  • By the polynomial division algorithm, any polynomial p(x)p(x) can be expressed as:

    p(x)=(x−r)q(x)+k

    p(x)=(xr)q(x)+k

    where q(x)q(x) is the quotient and kk is the remainder.

  • If rr is a root of p(x)p(x), then k=0k = 0, making p(x)p(x) completely factored.

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