A binomial has been partially factored, as shown below:x2 − 25 = (x + 5)(_____)Which of the following binomials represents the missing factor? (x − 5) (x + 5) (x − 20) (x + 20)
Question
A binomial has been partially factored, as shown below:x2 − 25 = (x + 5)(_____)Which of the following binomials represents the missing factor? (x − 5) (x + 5) (x − 20) (x + 20)
Solution
Para resolver el problema, sigamos estos pasos:
- Identifiquemos la forma factorizada del binomio dado. La expresión original es .
- Reconozcamos que es una diferencia de cuadrados. La fórmula general para la diferencia de cuadrados es .
- En este caso, y , ya que .
- Sustituyamos y en la fórmula de la diferencia de cuadrados: .
Por lo tanto, el binomio que representa el factor faltante es .
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