Polynomials & Partial Fractions
Polynomial Division
![Rendered by QuickLaTeX.com P(x)=\text{divisor}\times Q(x)+R(x)](https://teach.sg/wp-content/ql-cache/quicklatex.com-72986e45cc53451f2beed2c7298b7ed6_l3.png)
Remainder Theorem
If
is divided by
, remainder is
.
If
is divided by
, remainder is
.
![Rendered by QuickLaTeX.com P(x)](https://teach.sg/wp-content/ql-cache/quicklatex.com-d0da22b6347dac80d8c7d5e155a8bf81_l3.png)
![Rendered by QuickLaTeX.com x-c](https://teach.sg/wp-content/ql-cache/quicklatex.com-4730609edf479bf0589df3227ede77fa_l3.png)
![Rendered by QuickLaTeX.com \text{f}(c)](https://teach.sg/wp-content/ql-cache/quicklatex.com-1ae16c2da2cacb45af512b2d9cd0031d_l3.png)
If
![Rendered by QuickLaTeX.com P(x)](https://teach.sg/wp-content/ql-cache/quicklatex.com-d0da22b6347dac80d8c7d5e155a8bf81_l3.png)
![Rendered by QuickLaTeX.com ax-b](https://teach.sg/wp-content/ql-cache/quicklatex.com-5562eabcf02634402b891ef15a3cde41_l3.png)
![Rendered by QuickLaTeX.com \text{f}\left(\dfrac{b}{a}\right)](https://teach.sg/wp-content/ql-cache/quicklatex.com-21753c6c49419007e86c61f374b6f4e2_l3.png)
Factor Theorem
If
is a factor of
,
.
If
is a factor of
,
.
![Rendered by QuickLaTeX.com x-c](https://teach.sg/wp-content/ql-cache/quicklatex.com-4730609edf479bf0589df3227ede77fa_l3.png)
![Rendered by QuickLaTeX.com P(x)](https://teach.sg/wp-content/ql-cache/quicklatex.com-d0da22b6347dac80d8c7d5e155a8bf81_l3.png)
![Rendered by QuickLaTeX.com \text{f}(c)=0](https://teach.sg/wp-content/ql-cache/quicklatex.com-bd63e359bfa42386ba2cb33efa573298_l3.png)
If
![Rendered by QuickLaTeX.com ax+b](https://teach.sg/wp-content/ql-cache/quicklatex.com-a7c4aa7abf5cea314a91c3c49a5a5cf4_l3.png)
![Rendered by QuickLaTeX.com P(x)](https://teach.sg/wp-content/ql-cache/quicklatex.com-d0da22b6347dac80d8c7d5e155a8bf81_l3.png)
![Rendered by QuickLaTeX.com \text{f}\left(-\dfrac{b}{a}\right)=0](https://teach.sg/wp-content/ql-cache/quicklatex.com-8af3ae6ee506164c1cd47daced718833_l3.png)
Cubic Polynomials
![Rendered by QuickLaTeX.com a^3+b^3 = (a+b)(a^2-ab+b^2)](https://teach.sg/wp-content/ql-cache/quicklatex.com-f59941d7964b8a68e1013f8623b7b21a_l3.png)
![Rendered by QuickLaTeX.com a^3-b^3 = (a-b)(a^2+ab+b^2)](https://teach.sg/wp-content/ql-cache/quicklatex.com-c67a4177f31b410a61e62c5ed6e9ac3c_l3.png)
Partial Fractions
![Rendered by QuickLaTeX.com 1.\,\dfrac{f(x)}{(ax + b)(cx+d)} = \dfrac{A}{ax+b} + \dfrac{B}{cx+d}](https://teach.sg/wp-content/ql-cache/quicklatex.com-35f3b961dc4d107869f57bc3267ddc6a_l3.png)
![Rendered by QuickLaTeX.com 2.\,\dfrac{f(x)}{(ax + b)(cx+d)^2} = \dfrac{A}{ax+b} + \dfrac{B}{cx+d} + \dfrac{C}{({cx+d})^2}](https://teach.sg/wp-content/ql-cache/quicklatex.com-c9bec99002fd68751684e698421ea958_l3.png)
![Rendered by QuickLaTeX.com 3.\,\dfrac{f(x)}{(ax + b)(x^2+c)} = \dfrac{A}{ax+b} + \dfrac{Bx+C}{x^2+c}](https://teach.sg/wp-content/ql-cache/quicklatex.com-d9f4a9924f0a444c34d3b96773481514_l3.png)
*
![Rendered by QuickLaTeX.com \dfrac{f(x)}{(ax + b)(x^2)} = \dfrac{A}{ax+b} + \dfrac{B}{x}+\dfrac{C}{x^2}](https://teach.sg/wp-content/ql-cache/quicklatex.com-40ce3ba06d0395f106634374618ff4af_l3.png)