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EXPRESIONES ALGEBRAICAS
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Teorema del resto. Para calcular el resto de la división de un polinomio P(x) entre x-a basta sustituir en P(x) la x por a.
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El resto de la división P (x): (x – 8) es 0 y, por tanto, la división es exacta.
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: ( x – 3 )
3 es divisor de 30, pero no es raíz del polinomio dividendo. 5 es divisor de 30, y es raíz del polinomio dividendo.
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Para factorizar polinomios, dispones de algunos recursos:
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Vemos que la división del polinomio A (x) entre (x + 1) es exacta, lo que nos permite una primera descomposición: A (x) = x 4 – 2x 3– 2x 2– 2x – 3 = (x + 1) · (x 3 – 3x 2 + x – 3) Seguimos el mismo proceso con el polinomio C (x) = x 3 – 3x 2 + x – 3, y vemos que la división entre (x – 3) es exacta: C (x) = x 3 – 3x 2 + x – 3 = (x – 3) · (x 2 + 0x + 1) A (x) = (x + 1) · (x 3 – 3x 2 + x – 3) = (x + 1) · (x – 3) · (x 2 + 1)El último factor, (x 2 + 1), no se puede descomponer, pues no hay ningún valor de x que lo anule. Es decir, no tiene raíces.
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