Question

Dau coroană
Urgent
repede
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Answer 1

a) f(-1) = (-1)³ - 3(-1)² - 4(-1) + 12 = - 1 - 3 + 4 + 12 = 16 - 4 = 12

b)

$X^{3} - 3X^{2} - 4X + 12 = X^{3} - 5X^{2} + 2X^{2} - 10X - 3X + 15 + 9X - 3 = X^{2}(X - 5) + 2(X - 5) - 3(X - 5) + 9X - 3 = (X - 5)(X^{2} + 2X - 3) + 9X - 3$

=>

$(X^{3} - 3X^{2} - 4X + 12) : (X^{2} + 2X - 3) = \bf X - 5 \ \ rest \ \ 9X - 3$

c)

$X^{3} - 3X^{2} - 4X + 12 = X^{2}(X - 3) - 4(X - 3) = (X - 3)(X^{2} - 4) = (X - 3)(X - 2)(X + 2)$