When performing long division on polynomials, it can be written in this structure: \( \begin{array}{r}
3x \ + \ 5 \\
x^2 - 3x \enclose{longdiv}{ \ \ 3x^3 \ - \ 4x^2 \ + \ 5x \ + \ 4} \\
\underline{-(3x^3 - 9x^2) \hspace{4.7em} }\\
5x^2 \ + \ 5x \hspace{2.2em} \\
\underline{-(5x^2 \ - 15x) \hspace{1.8em} }\\
\underline{20x \ + \ 4} \\
\end{array} \) In this example: Dividend: \( \quad 3x^3 - 4x^2 + 5x +4 \quad\) which is the polynomial that is being divided Divisor: \( \quad \quad x^2 - 3 \quad \quad \quad \quad \quad \quad \ \) is what the polynomial is divided by Quotient: \( \quad \ 3x + 5 \quad \quad \quad \quad \quad \quad\) the solution of the division Remainder: \( \ 20x + 4\) It can be expressed in the following equation: \( \underbrace{3x^3 - 4x^2 + 5x + 4}_{Dividend} = \underbrace{(x^2 - 3)}_{Divisor} \times \underbrace{(3x + 5)}_{Quotient} + \underbrace{(20x + 4)}_{Remainder} \) In other words: \( \mathrm{Dividend} = \mathrm{Divisor} \times \mathrm{Quotient} + \mathrm{Remainder} \)

When performing long division on polynomials, it can be written in this structure:
\( \begin{array}{r}
3x \ + \ 5 \\
x^2 - 3x \enclose{longdiv}{ \ \ 3x^3 \ - \ 4x^2 \ + \ 5x \ + \ 4} \\
\underline{-(3x^3 - 9x^2) \hspace{4.7em} }\\
5x^2 \ + \ 5x \hspace{2.2em} \\
\underline{-(5x^2 \ - 15x) \hspace{1.8em} }\\
\underline{20x \ + \ 4} \\
\end{array} \)
In this example: 
**Dividend:** \( \quad 3x^3 - 4x^2 + 5x +4 \quad\)  which is the polynomial that is being divided
**Divisor:** \( \quad \quad x^2 - 3 \quad \quad \quad \quad \quad \quad \ \) is what the polynomial is divided by
**Quotient:** \( \quad \ 3x + 5 \quad \quad \quad \quad \quad \quad\) the solution of the division
**Remainder:** \( \ 20x + 4\)
It can be expressed in the following equation:
\( \underbrace{3x^3 - 4x^2 + 5x + 4}_{Dividend} = \underbrace{(x^2 - 3)}_{Divisor} \times \underbrace{(3x + 5)}_{Quotient} + \underbrace{(20x + 4)}_{Remainder} \)
In other words:
\( \mathrm{Dividend} = \mathrm{Divisor} \times \mathrm{Quotient} + \mathrm{Remainder} \)

Long Division of Polynomials

Long Division of Polynomials