Polynomial Division Calculator

Your details

The highest power of x in the dividend P(x).
The highest power of x in the divisor Q(x). Must be less than or equal to the dividend degree.
QuotientHas remainder
x^2 - 4

The polynomial A(x) such that P(x) = A(x) * Q(x) + R(x)

Remainder-4
Full expressionP(x) = (x^2 - 4) * Q(x) + (-4)
Is divisor a factor?No - the remainder is non-zero
Remainder (numeric)-4
Quotient degree2
Quotient degree2
Remainder value-4

Division yields quotient x^2 - 4 with remainder -4.

  • The quotient has degree 2, which is deg(P) - deg(Q) = 3 - 1 = 2.
  • The remainder is -4. Any root of Q(x) substituted into P(x) will give this value (remainder theorem).
  • The root of Q(x) is x = 2. Plugging this into P(x) gives the remainder -4.
  • Check your answer: multiply the quotient by Q(x) and add the remainder - the result should equal P(x).

Next stepIf you need an exact division, adjust the coefficients of P(x) to make the remainder zero.

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