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I broke up the chemical and metallurgical division that Walt had been running and spun out the high-growth plastics business. I put Chuck Carson, who had run our laminates business, over the slower-growing but highly profitable remaining materials businesses.

The excerpt above is from the book Jack: Straight from the Gut. The word "business" has many meanings.

Could you tell me what they mean here? Why does the last sentence use the plural form of "business"?

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cat fold 525Could you tell me what they mean here?

It means a commercial enterprise.

Take a look at entry #2.2 in the link below.

https://en.oxforddictionaries.com/definition/business

cat fold 525Why does the last sentence use the plural form of "business"?

It refers to many businesses. Presumably, that company has more than one materials division/business.