Question

How do you divide $\dfrac{4{{x}^{3}}+3{{x}^{2}}-3x+14}{x+2}$?

Answer 1

Hint: We will use the polynomial long division method to solve the given expression. First we will divide the first term of the dividend by divisor and put the quotient above the line. Then multiply the quotient by divisor and place the result under the dividend and subtract the terms. Then pull down the next term from the dividend and repeat the process to get the desired answer.

Complete step-by-step solution:
We have been given an expression $\dfrac{4{{x}^{3}}+3{{x}^{2}}-3x+14}{x+2}$.
We have to divide the expression.
We will solve the given expression by using the long division method.
For long division method we have to follow some steps as follows:
First we divide the tens column dividend by the divisor. Then multiply the divisor by the quotient in the tens place column. Then subtract the product from the divisor and bring down the dividend in the ones column and repeat the process till no term left in the divisor column.
Now, let us start dividing the terms by long division method. Then we will get
\[x+2\overset{4{{x}^{2}}-5x+7}{\overline{\left){\begin{align}
  & 4{{x}^{3}}+3{{x}^{2}}-3x+14 \\
 & \underline{4{{x}^{3}}+8{{x}^{2}}} \\
 & -5{{x}^{2}}-3x \\
 & -5{{x}^{2}}-10x \\
 & \underline{\overline{\begin{align}
  & 7x+14 \\
 & 7x+14 \\
\end{align}}} \\
 & 0 \\
\end{align}}\right.}}\]
So on dividing the given expression $\left( 5{{x}^{4}}+14{{x}^{3}}+9x \right)\div \left( {{x}^{2}}+3x \right)$ by using long division method we get the quotient as \[4{{x}^{2}}-5x+7\].

Note: The point to be noted is that if the terms are not in decreasing power of variable then we need to arrange the terms in decreasing power of the variable order including the missing terms. Then we need to divide the terms by following the steps.