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JAMB 2011 · UTME · Q13

Find the remainder when x3−2x2+3x−3x^3 - 2x^2 + 3x - 3 is divided by x2+1x^2 + 1.

Worked solution (try it first)
  1. Long division: x3÷x2=xx^3 \div x^2 = x.
  2. Subtract x(x2+1)=x3+xx(x^2 + 1) = x^3 + x to leave −2x2+2x−3-2x^2 + 2x - 3.
  3. −2x2÷x2=−2-2x^2 \div x^2 = -2.
  4. Subtract −2(x2+1)=−2x2−2-2(x^2 + 1) = -2x^2 - 2 to leave 2x−12x - 1.
  5. 2x−12x - 1 has a lower power than x2+1x^2 + 1, so it is the remainder, option A.

Also set as JAMB 2017 · UTME · Q39

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