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5. Factorizar la siguiente expresión algebraica:

[tex] x^4 + 3x [/tex]

Sagot :

GinnyAnswer
Para factorizar la expresión algebraica [tex]\(x^4 + 3x\)[/tex], sigamos estos pasos:

1. Identificación de un factor común: Observamos que tanto [tex]\(x^4\)[/tex] como [tex]\(3x\)[/tex] tienen [tex]\(x\)[/tex] como factor común.

2. Extracción del factor común: Tomamos [tex]\(x\)[/tex] como factor común. Entonces, la expresión se puede reescribir como:
[tex]\[ x^4 + 3x = x(x^3) + x(3) \][/tex]
Esto se simplifica a:
[tex]\[ x(x^3 + 3) \][/tex]

3. Resultado final: La expresión factorada es:
[tex]\[ x(x^3 + 3) \][/tex]

Por lo tanto, la factorización de la expresión [tex]\(x^4 + 3x\)[/tex] es:
[tex]\[ x(x^3 + 3) \][/tex]
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