Dividing Polynomials | Algebra Math Help

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Dividing Polynomials | Algebra Math Help

What is a polynomial?

A polynomial is an expression of at least two terms that is made up of variables and coefficients and uses only the operations of addition, subtraction or multiplication. An example of a polynomial is:

x^{3} +5x^{2} -2x-24

How To Divide Polynomials:

\begin{array}{l} In\ the\ example\ ( x³\ +\ 5x²\ -2x\ –\ 24) \ divided\ by\ ( x\ –\ 2) ,\ \\ the\ divisor\ will\ be\ ( x\ -\ 2) \ and\ the\ dividend\ will\ be\ ( x³\ +\ 5x²\ -2x\ –\ 24)\\ To\ divide,\ first\ take\ the\ first\ term\ of\ the\ dividend\ and\ divide\ it\ by\ the\ first\ term\ of\ \\ the\ divisor.\ In\ this\ example\ you\ will\ divide\ x³\ by\ x.\ This\ equals\ x².\ \\ This\ is\ going\ to\ be\ the\ first\ part\ of\ the\ quotient. \end{array}

\begin{array}{l} Next,\ Multiply\ the\ divisor\ by\ the\ first\ term\ of\ the\ quotient\ and\ put\ that\ answer\ \\ under\ the\ first\ two\ terms\ of\ the\ dividend.\ Now\ subtract. \end{array}

\begin{array}{l} After\ you\ subtract,\ bring\ down\ the\ next\ term\ of\ the\ dividend\ and\ start\ the\ process\ again. \end{array}

\begin{array}{l} Now\ take\ the\ first\ term\ of\ the\ new\ dividend\ and\ divide\ it\ by\ the\ first\ term\ of\ the\ divisor.\\ This\ is\ going\ to\ be\ the\ next\ term\ of\ the\ quotient. \end{array}

Now\ multiply\ and\ subtract.

After\ you\ subtract,\ bring\ down\ the\ next\ term\ of\ the\ dividend.

\begin{array}{l} Now\ take\ the\ first\ term\ of\ the\ new\ dividend\ and\ divide\ it\ by\ the\ first\ term\ of\ the\ divisor.\\ This\ is\ going\ to\ be\ the\ next\ term\ of\ the\ quotient. \end{array}

Now\ multiply\ and\ subtract.

\begin{array}{l} There\ are\ no\ more\ terms\ to\ bring\ down,\ so\ we\ are\ done\ dividing.\\ \ In\ this\ example\ there\ is\ no\ remainder\ and\ the\ quotient\ is\ x²+7x+12.( x³\ +\ 5x²\ -2x\ –\ 24)\\ \ divided\ by\ ( x\ –\ 2) \ equals\ x²+7x+12. \end{array}

Sample Math Problems

1) Use long division to find the quotient.

( \ x²\ –\ 3x\ –\ 10) \ \div \ ( x\ +\ 2)

Solution:

First take the first term of the dividend and divide it by the first term of the divisor.