Polynomial Division Calculator
This calculator computes polynomial division to determine the quotient and remainder.
- \(\displaystyle \small{x^2+5x+6\rightarrow} \) x^2+5x+6
- \(\displaystyle \small{x^2-\frac{5}{3}x-\frac{2}{3}\rightarrow} \) x^2-(5/3)x-(2/3)
- \(\displaystyle \small{x^{10}-1\rightarrow} \) x^10-1
- The character allowed is only \(x\).
- the maximum degree for each expression is 10.
- Represent exponentiation with ^.
- Use only () for parentheses.
- Polynomial Factorization Calculator is available at this link.
What is polynomial division?
Polynomials can be used to compute the quotient and remainder, as in integer division.
Such division is called polynomial division.
If the expression to be divided is \(\mathrm{A}\), the expression to be divided is \(\mathrm{B}\), the quotient is \(\mathrm{C}\), and the remainder is \(\mathrm{D}\), the following equation is obtained.
\[ \mathrm{A}=\mathrm{B}\times\mathrm{C}+\mathrm{D} \]
Example
Example 1
Find the quotient and remainder of \( x^{3}+1 \) divided by \( x-1 \).
Solution
\(\displaystyle \text{Quotient : }x^{2}+x+1 \)
\(\displaystyle \text{Remainder : }2 \)
Example 2
Find the quotient and remainder of \(\displaystyle \frac{1}{2}x^{2}+x+\frac{1}{2} \) divided by \(\displaystyle x-1 \).
Solution
\(\displaystyle \text{Quotient : }\frac{1}{2}x+\frac{3}{2} \)
\(\displaystyle \text{Remainder : }2 \)