Factorizacion :
<img src="https://tex.z-dn.net/?f=P%28x%29%3D3x%5E3%2B7x%5E2-7x-3%20%5CRightarrow%203x%5E3-3%2B7x%5E2-7x%20%5C%5C%20%5C%5C%203%28x%5E3-3%29%2B7x%28x-1%29%20" />
<img src="https://tex.z-dn.net/?f=%28x%5E3-1%29%3D%28x-1%29%28x%5E2%2Bx%2B1%29%20%20" />
<img src="https://tex.z-dn.net/?f=3%28x-1%29%28x%5E2%2Bx%2B1%29%2B7x%28x-1%29%5CRightarrow%20%28x-1%29%5C%5B3%28x%5E2%2Bx%2B1%29%2B7x%29%5C%5D%20%5CRightarrow%20%28x-1%29%283x%5E2%2B3x%2B3%2B7x%29%5CRightarrow%20%28x-1%29%283x%5E2%2B10x%2B3%29" />
resolución por la fórmula cuadrática
<img src="https://tex.z-dn.net/?f=3x%5E2%2B10x%2B3%3D3%28x%2B3%29%28x%2B%5Cfrac%7B1%7D%7B3%7D%29%3D%28x%2B3%29%283x%2B1%29" />
<img src="https://tex.z-dn.net/?f=P%28x%29%3D%28x-1%29%28x%2B3%29%283x%2B1%29" />
<img src="https://tex.z-dn.net/?f=Q%28x%29%3D5x%5E4-15x%5E2-10x%20%5CRightarrow%205x%28x%5E3-3x-2%29" />
por resolución de gauss para factorizar y ruffini :
<img src="https://tex.z-dn.net/?f=x%5E3-3x-2" /> las raíces son <img src="https://tex.z-dn.net/?f=x_1%3D-1%20%5C%3B%5C%20x_2%3D2%20%20%5C%20%3B%20%5C%20x_3%3D-1%5CRightarrow%20%28x-2%29%28x%2B1%29%5E2" />
<img src="https://tex.z-dn.net/?f=Q%28x%29%3D5x%28x-2%29%28x%2B1%29%5E2%20" />.