How to divide the equation in algebraic expression.

Hint: To divide an equation in algebraic expression we use a long division method. Firstly we write the polynomial in descending order then firstly we find a factor that satisfies the equation using hit and trial method. Then we will use that factor to divide the equation in algebraic expression.

Complete step-by-step solution:
To divide the equation in algebraic expression find a factor of that equation by hit and trial method and then divide the equation by that factor as follows:
1. Arrange the polynomial in descending order of both the Dividend and the divisor.
2. Divide the first term of the dividend by the first term of the divisor by finding a term which when multiplied by the first term of the divisor makes it equal to the first term of the dividend.
3. Multiply the number obtains in step 2 by the divisor and subtracts it by the dividend and brings the remaining term down.
4. Repeat step 2 and 3 till we get our remainder as zero or till we have taken all the terms down.
5. Multiply the quotient obtained and the factor we got from hit and trial method and get the equation in algebraic expression.
 For example- Divide equation ${{x}^{2}}+5x+6$ in algebraic expression.
We have to divide the below equation:
${{x}^{2}}+5x+6$…..$\left( 1 \right)$
By using hit and trial method put $x=-2$ in equation (1)
$\begin{align}
  & \Rightarrow {{\left( -2 \right)}^{2}}+5\times -2+6 \\
 & \Rightarrow 4-10+6 \\
 & \Rightarrow 0 \\
\end{align}$
So $\left( x+2 \right)$ is one of the factors now we will divide the equation (1) by $\left( x+2 \right)$ as below:
$x+2\overset{x+3}{\overline{\left){\begin{align}
  & {{x}^{2}}+5x+6 \\
 & \underline{{{x}^{2}}+2x} \\
 & 0+3x+6 \\
 & \underline{0+3x+6} \\
 & 0+0+0 \\
\end{align}}\right.}}$
So we get the Quotient as $\left( x+3 \right)$
So we can divide equation ${{x}^{2}}+5x+6$ as an algebraic expression$\left( x+2 \right)\left( x+3 \right)$
Hence we have to divide the dividend that is our equation by a divisor that is one of the factors of the equation to divide the equation in algebraic expression

Note: Algebraic expression is an expression which is made up of variables and constant along with algebraic operations which are addition, subtraction, multiplication and division. Algebraic equation is the equation made up of variables and constant and is equal to 0.