27.1 Long division in polynomial functions
Long division in polynomial functions
It may sound hard, but the idea of polynomial long division is basically the same as any other long divisions. A division statement has 4 elements: dividend, division, quotient, and remainder.
Basic concepts:
 Simplifying rational expressions and restrictions
 Dividing rational expressions
 Dividing functions
Related concepts:
 Integration of rational functions by partial fractions
Lessons
Notes:
A division statement can be written in 2 ways:
i) dividend = (divisor) (quotient) + remainder
ii) $\frac{dividend}{divisor}$ = quotient + $\frac{remainder}{divisor}$

a)
Operate long division

b)
Identify:
• Dividend:
• Division:
• Quotient:
• Remainder: 
c)
Write the division statement in 2 ways.


b)
$\left( {  {x^2} + 6x  2} \right) \div \left( x \right)$

3.
Operate long division.

a)
$\left( {{x^3} + 5x  11} \right) \div \left( {x  2} \right)$

c)
$\left( {4{x^3} + 6{x^2}  9x + 5} \right) \div \left( {2{x^2}  1} \right)$


a)
Operate long division.

b)
Write the division statement.

c)
Is $\left( {3x + 5} \right)$ a factor of $\left( {6{x^2} + 7x  5} \right)$? Explain.
