Partial fractions

When is a fraction improper?

When the highest degree on the numerator is greater than or equal to the highest degree on the denominator

how do you do polynomial division when the divisor is quadratic

just the same as normal - always divide by your highest power term

how do you do partial fractions for an improper fraction? NAMES OF METHODS

long divison or form

How do you use long division for partial fractions for improper fractions

normal long division and stop when your divisors highest power is greater than the dividend term and then put the remainder over the divisor

What is the common form of improper partial fractions with no degree difference between nom and denom?

A + B/factor + C/factor

cover up method for checking (NO METHOD MARKS IF WRONG)

cover the denom of one term in both LHS and RHS and input whatever makes that denom zero to find the numerator value. Numerator value of that part = evaluated LHS (COVERED UP TERM)

How to find the terms which aren’t fractions (for improper fractions) with the coverup method

use long division

What is the general form of improper partial fractions

(x expression (order of the gap between orders of nom and denom) then the fractions