Question

Помогите решить деление многочленов

Answer 1

$\displaystyle \tt a). \ \ \frac{3x^{3}+19x^{2}+22x-24}{x+3}=\frac{3x^{3}+21x^{2}-2x^{2}+36x-14x-24}{x+3}=\\\\\\{} \ \ =\frac{x^{2}(3x-2)+7x(3x-2)+12(3x-2)}{x+3}=\frac{(3x-2)(x^{2}+7x+12)}{x+3}=   \\\\\\{} \ \ =\frac{(3x-2)(x+3)(x+4)}{x+3}=(3x-2)(x+4);$

$\displaystyle \tt b). \ \ \frac{35x^{3}-124x^{2}-67x+12}{5x+3}=\frac{35x^{3}-5x^{2}-119x^{2}+17x-84x+12}{5x+3}=\\\\\\{} \ \ =\frac{5x^{2}(7x-1)-17x(7x-1)-12(7x-1)}{5x+3}=\frac{(7x-1)(5x^{2}-17x-12)}{5x+3}=\\\\\\{} \ \ =\frac{(7x-1)(5x+3)(x-4)}{5x+3}=(7x-1)(x-4);$

Answer 2

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