Faktorisasi Aljabar
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| Sumber Gambar : Google |
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$ 3x^{2}-2x-2 $
Jawab :
$ 3\left (x^{2}-\frac{2}{3}x-\frac{2}{3} \right ) $
$ =3\left \{ \left ( x-\frac{2}{3.2} \right )^{2}-\frac{2}{3}-\left ( \frac{2}{3.2} \right )^{2} \right \} $
$ =3\left \{ \left ( x-\frac{1}{3} \right )^{2}-\frac{2}{3} -\frac{1}{9}\right \} $
$ =3\left \{ \left ( x-\frac{1}{3} \right )^{2}-\frac{7}{9} \right \} $
$ =3\left \{ \left ( x-\frac{1}{3} \right )^{2}-\left ( \frac{\sqrt{7}}{3} \right )^{2} \right \} $
$ =3\left \{ \left ( x-\frac{1}{3}+\frac{\sqrt{7}}{3} \right )\left ( x-\frac{1}{3}-\frac{\sqrt{7}}{3} \right ) \right \} $
$ =\left ( 3x-1+\sqrt{7} \right )\left ( x-\frac{1}{3}-\frac{\sqrt{7}}{3} \right ) $
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