Fandom

Math Wiki

Polynomial

1,014pages on
this wiki
Add New Page
Talk0 Share

A polynomial is an expression formed from one or more terms and constants by addition, each term of which should contain a variable raised to a non-negative integer power.

Formal Definition

Let R be a ring (such as the real numbers, rational numbers, or integers). Now let n be a natural number and a_0,a_1,\dots,a_n be elements of R. Then the function p:R\rightarrow R defined by:

p\left(x\right)=\sum_{k=0}^{n}a_{k}x^{k}=a_{n}x^{n}+a_{n-1}x^{n-1}+\dots+a_{2}x^{2}+a_{1}x+a_{0}

For all x in R is said to be a polynomial function in a single variable.

Moreover, if a_n\ne 0, we say that p is an nth-degree polynomial.

We denote the set of polynomials as R\left[x\right].

Polynomial long division

\frac{2x^4+2x^3-3x^3-2x+1}{x^2-1}

Dividing a polynomial follows a process similar to long division.

\begin{align}
        &   &      &       & +2x^2 & +2x & -1\\
\hline
x^2 - 1 & | & 2x^4 & +2x^3 & -3x^2 & -2x & +1\\
        &   &-2x^4 &       & +2x^2 &     &  \\
\hline
        &   &      & +2x^3 &  -x^2 & -2x & +1\\
        &   &      & -2x^3 &       & +2x &  \\
\hline
        &   &      &       &  -x^2 & & +1\\
        &   &      &       &  -x^2 & & +1\\
\hline
        &   &      &       &       & & 0
\end{align}

See also

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.