7. Polinoma dalīšana ar monomu

Lai polinomu izdalītu ar monomu, ar monomu jādala katrs polinoma loceklis, un iegūtie dalījumi jāsaskaita.

(ab + ac) : a = ab : a + ac : a = \frac{a b}{a} + \frac{a c}{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) (28 a^{5} + 14 ab) : 7 = 28 a^{5} : 7 + 14 ab : 7 = \frac{{}^{4}28 a^{5}}{{}^{1}7} + \frac{{}^{2}14 ab}{{}^{1}7} = 4 a^{5} + 2 ab

\begin{array}{l} b) (5 x^{3} y - 3 x^{4}) : 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 xy - 3 x^{2} \end{array}

\begin{array}{l} c) (10 x^{4} y - 5 x^{2} y^{2}) : 5 x^{2} y = 10 x^{4} y : 5 x^{2} y - 5 x^{2} y^{2} : 5 x^{2} y = \frac{{}^{2}10 x^{4} y}{{}^{1}5 x^{2} y} - \frac{{}^{1}{5 x^{2}} y^{2}}{{}^{1}{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}

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