How to Say "they seek" in Spanish
The Spanish word for “they seek” is “buscan” — A1 level. This is a very common word in everyday Spanish.

Examples
Mis padres buscan una casa más grande.
My parents are looking for a bigger house.
¿Qué buscan ustedes en esta tienda?
What are you (all, formal) looking for in this store?
Los científicos buscan la cura para esa enfermedad.
The scientists seek the cure for that disease.
Who is 'buscan'?
'Buscan' means 'they look for' (ellos/ellas) or the formal 'you look for' (ustedes). It describes an action done by a group of people.
No Preposition Needed
Unlike English ('look for'), the Spanish verb 'buscar' doesn't need a small connecting word (preposition) before the thing being searched for.
Adding 'por'
Mistake: “Ellos buscan *por* la llave.”
Correction: Ellos buscan la llave. (Do not add 'por'—the verb 'buscar' already includes the meaning of 'for.')
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