# Polynomial long division

##### Intros
###### Lessons
1. Review: Long division with numbers
long division with polynomials works in the same way as long division with numbers
exercise:
658 ÷ 20
i) Operate long division
ii) Identify:
• Dividend:
• Division:
• Quotient:
• Remainder:
iii) Write the division statement in 2 ways.
##### Examples
###### Lessons
1. Use long division to divide polynomials
Apply long division, and then use the result to write the division statement in 2 ways.
1. $\left( {8{x^3} - 14{x^2} + 7x - 1} \right) \div \left( {2x - 5} \right)$
2. $\left( { - {x^2} + 6x - 2} \right) \div \left( x \right)$
2. Watch out for "Missing Terms"! → Use "Placeholder"
Operate long division.
1. $\left( {29{x^3} - 12{x^4} - x} \right) \div \left( { - 3x + 5} \right)$
2. $\left( {{x^3} + 5x - 11} \right) \div \left( {x - 2} \right)$
3. $\left( {4{x^3} + 6{x^2} - 9x + 5} \right) \div \left( {2{x^2} - 1} \right)$
3. Application of a Division Statement
Given the long division as shown:

Determine the polynomial $P\left( x \right)$.
1. Determine "Factors"
$\left( {6{x^2} + 7x - 5} \right) \div \left( {3x + 5} \right)$
1. Operate long division.
2. Write the division statement.
3. Is $\left( {3x + 5} \right)$ a factor of $\left( {6{x^2} + 7x - 5} \right)$? Explain.