Descompunem în factori primi:
[tex]a) = (x-1)^3 - 16(x-1)[/tex]
[tex]= (x-1) \cdot \big[(x-1)^2-4^2\big][/tex]
[tex]= (x-1) \cdot (x-1-4) \cdot (x-1+4)[/tex]
[tex]= (x-1) \cdot (x-5) \cdot (x+3)[/tex]
[tex]= [x+(-1)] \cdot [x+(-5)] \cdot (x+3)[/tex]
[tex]\bf a = -1; \ b = -5; \ c = 3[/tex]
[tex]b) = (x + 2)^3 - 9(x + 2)[/tex]
[tex]= (x + 2) \cdot \big[(x + 2)^2 - 3^2\big][/tex]
[tex]= (x + 2) \cdot (x + 2 - 3) \cdot (x + 2 + 3)[/tex]
[tex]= (x + 2) \cdot (x - 1) \cdot (x + 5)[/tex]
[tex]= (x + 2) \cdot [x + (-1)] \cdot (x + 5)[/tex]
[tex]\bf a = 2; \ b = -1; \ c = 5[/tex]
[tex]c) = (2x - 3)^3 - 4(2x - 3)[/tex]
[tex]= (2x - 3) \cdot \big[(2x - 3)^2 - 2^2\big][/tex]
[tex]= (2x - 3) \cdot (2x - 3 - 2) \cdot (2x - 3 + 2)[/tex]
[tex]= (2x - 3) \cdot (2x - 5) \cdot (2x - 1)[/tex]
[tex]= 2\bigg(x - \dfrac{3}{2} \bigg) \cdot 2\bigg(x - \dfrac{5}{2}\bigg) \cdot 2\bigg(x - \dfrac{1}{2}\bigg)[/tex]
[tex]= 8\bigg(x - \dfrac{3}{2} \bigg) \cdot \bigg(x - \dfrac{5}{2}\bigg) \cdot \bigg(x - \dfrac{1}{2}\bigg)[/tex]
[tex]\bf a = -\dfrac{3}{2}; \ b = -\dfrac{5}{2}; \ c = -\dfrac{1}{2}[/tex]
[tex]d) = (3x - 2)^3 - 9(3x - 2)[/tex]
[tex]= (3x - 2) \cdot \big[(3x - 2)^2 - 3^2\big][/tex]
[tex]= (3x - 2) \cdot (3x - 2 - 3) \cdot (3x - 2 + 3)[/tex]
[tex]= (3x - 2) \cdot (3x - 5) \cdot (3x + 1)[/tex]
[tex]= 3\bigg(x - \dfrac{2}{3} \bigg) \cdot 3\bigg(x - \dfrac{5}{3}\bigg) \cdot 3\bigg(x + \dfrac{1}{3}\bigg)[/tex]
[tex]= 27\bigg(x - \dfrac{2}{3} \bigg) \cdot \bigg(x - \dfrac{5}{3}\bigg) \cdot \bigg(x + \dfrac{1}{3}\bigg)[/tex]
[tex]\bf a = -\dfrac{2}{3}; \ b = -\dfrac{5}{3}; \ c = \dfrac{1}{3}[/tex]
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