Polynomials & Partial Fractions

Polynomial Division
P(x)=\text{divisor}\times Q(x)+R(x)
Remainder Theorem
If P(x) is divided by x-c, remainder is \text{f}(c).
If P(x) is divided by ax-b, remainder is \text{f}\left(\dfrac{b}{a}\right).
Factor Theorem
If x-c is a factor of P(x), \text{f}(c)=0.
If ax+b is a factor of P(x), \text{f}\left(-\dfrac{b}{a}\right)=0.
Cubic Polynomials
a^3+b^3 = (a+b)(a^2-ab+b^2)
a^3-b^3 = (a-b)(a^2+ab+b^2)
Partial Fractions
1.\,\dfrac{f(x)}{(ax + b)(cx+d)} = \dfrac{A}{ax+b} + \dfrac{B}{cx+d}
2.\,\dfrac{f(x)}{(ax + b)(cx+d)^2} = \dfrac{A}{ax+b} + \dfrac{B}{cx+d} + \dfrac{C}{({cx+d})^2}
3.\,\dfrac{f(x)}{(ax + b)(x^2+c)} =  \dfrac{A}{ax+b} + \dfrac{Bx+C}{x^2+c}
*\dfrac{f(x)}{(ax + b)(x^2)} =  \dfrac{A}{ax+b} + \dfrac{B}{x}+\dfrac{C}{x^2}
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