### Teorija

Polinoma dalīšana ar monomu
"Lai polinomu izdalītu ar monomu, ar monomu jādala katrs polinoma loceklis un iegūtie dalījumi jāsaskaita."
$\left(\mathit{ab}+\mathit{ac}\right):a=\mathit{ab}:a+\mathit{ac}:a=\frac{\overline{)a}b}{\overline{)a}}+\frac{\overline{)a}c}{\overline{)a}}=b+c$
Atceries, ka, dalot pakāpes ar vienādām bāzēm, to kāpinātājus atņem.
$\frac{{a}^{m}}{{a}^{n}}={a}^{m}:{a}^{n}={a}^{m-n}$

Piemērs:
$a\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\left(28{a}^{5}+14\mathit{ab}\right):7=28{a}^{5}:7+14\mathit{ab}:7=\frac{4\phantom{\rule{0.147em}{0ex}}\overline{)28}{a}^{5}}{\overline{)7}\phantom{\rule{0.147em}{0ex}}1}+\frac{2\phantom{\rule{0.147em}{0ex}}\overline{)14}\mathit{ab}}{\overline{)7}\phantom{\rule{0.147em}{0ex}}1}=4{a}^{5}+2\mathit{ab}$

$\begin{array}{l}b\right)\phantom{\rule{0.294em}{0ex}}\left(5{x}^{3}y-3{x}^{4}\right):{x}^{2}=5{x}^{3}y:{x}^{2}-3{x}^{4}:{x}^{2}=\\ \\ =5{x}^{3-2}y-3{x}^{4-2}=5{x}^{1}y-3{x}^{2}=5\mathit{xy}-3{x}^{2}\end{array}$

$\begin{array}{l}c\right)\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\left(10{x}^{4}y-5{x}^{2}{y}^{2}\right):5{x}^{2}y=10{x}^{4}y:5{x}^{2}y-5{x}^{2}{y}^{2}:5{x}^{2}y=\frac{2\phantom{\rule{0.147em}{0ex}}\overline{)10}{x}^{4}\overline{)y}}{1\phantom{\rule{0.147em}{0ex}}\overline{)5}{x}^{2}\overline{)y}}-\frac{1\phantom{\rule{0.147em}{0ex}}\overline{)5{x}^{2}}{y}^{2}}{1\phantom{\rule{0.147em}{0ex}}\overline{)5{x}^{2}}y}=\\ \\ =2{x}^{4}:{x}^{2}-{y}^{2}:y=2{x}^{4-2}-{y}^{2-1}=2{x}^{2}-{y}^{1}=2{x}^{2}-y\end{array}$

Atsauce:
Matemātika 7. klasei /Ilze France, Gunta Lāce, Ligita Pickaine, Anita Miķelsone - Lielvārde: Lielvārds, 2007. -140.lpp.