Yes it is quite possible to have a behavior driven by both extrinsic and intrinsic motivational factors.
Explanation:
Intrinsic motivation is something that forces you to do things which give you internal satisfaction. For example when you persuade your hobbies, it is driven by intrinsic motivation.
Extrinsic motivation is something that forces you to do things which make you earn rewards. For example, when you do job to earn money.
Now both extrinsic and intrinsic motivation can be found in someone's behavior at a time. For example, if someone likes to do interior decoration and feels internal satisfaction in decorating the rooms and areas, and he or she persuade his career in interior designing and starts a business or job to earn money through decorating people's houses, offices, etc, to earn money, then this is the perfect combination of behaviors having both intrinsic and extrinsic motivational factors.
Learn more about intrinsic and extrinsic motivation at:
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