Bethlehem Steel Corp. yesterday reported losses for the fourth quarter and for 1984, cut its dividend from 15 to 10 cents and said it expects to post another "significant" loss in the first quarter of 1985.

Bethlehem, the nation's third-largest steel producer behind United States Steel Corp. and LTV Corp., last posted a profit in 1981, $211 million.

In other earnings reports yesterday, The Du Pont Co. put preliminary net income at $306 million for the last three months of 1984, 10 percent below the $341 million earned in the same period of 1983, on sales of $8.8 billion, which dipped 3 percent from the previous year.

Xerox Corp., citing a poor performance by its insurance unit and the previously announced phaseout of its Shugart disk drive operations, reported it lost $12 million in the fourth quarter and had a 38 percent drop in profit for all of 1984.

Castle & Cooke Inc., the beleaguered San Francisco food-products company, reported a net loss of $63.8 million for the first six months of fiscal 1985.

* Bethlehem Steel Corp. said it had a net loss of $64.5 million ($1.51 per share) in the fourth quarter, compared with a loss of $27.4 million (69 cents) in the year-earlier period. Fourth-quarter sales fell to $1.19 billion from $1.32 billion.

For 1984, Bethlehem posted a net loss of $112.5 million ($2.91), an improvement fom the loss of $163.5 million ($3.92) the year before. Sales rose to $5.4 billion from $4.9 billion.

Donald Trautlein, Bethlehem's chairman and chief executive officer, said the board of directors decided it was "prudent" to reduce the quarterly dividend to 10 cents per common share "in view of the significant losses incurred by Bethlehem in the fourth quarter and for 1984 as a whole, and because another significant loss is expected for the first quarter of 1985."

The dividend had stood at 15 cents for two years.

Trautlein said Bethlehem's return to profitability depends on implementation of the Reagan administration's plan to reduce steel imports, excluding finished steel, to 18.6 percent of the U.S. market. During the first 11 months of 1984, imports took more than 26 percent of the U.S. market, Bethlehem said.

Trautlein blamed 1984's losses on both imports and "continuing high employment costs." The steel business operated at 53 percent capacity in the fourth quarter and 68 percent for 1984, compared with 48 and 49 percent in the fourth quarter and full year 1983.

* E. I. du Pont de Nemours & Co., based in Wilmington, Del., reported preliminary 1984 earnings of $1.4 billion despite sluggish second-half performance, up 27 percent from 1983, on sales of $35.9 billion.

Chairman Edward Jefferson said the company was able to report that earnings per-share for the year increased to $5.93 from $4.70 in 1983 despite reduced demand in the second half of 1984.

The company also announced that it was offering a one-time incentive program aimed at persuading as many as 6,500 employes to take early retirements.

The company estimated the program will cost $125 million, which will be charged to first-quarter earnings, but savings in the rest of 1985 will offset the cost. In 1986, savings should exceed $225 million, the company said.

* Xerox Corp. said that its loss for the three-month period ended Dec. 31 compared with a profit of $73 million (64 cents a share) in the same three months a year earlier.

Fourth-quarter revenue from continuing reprographics and information systems rose 14 percent, to $2.5 billion, from $2.2 billion a year earlier, the Stamford, Conn.-based company said in a statement released in New York. For 1984, the company said its net income fell to $291 million ($2.53) from $466 million ($4.42) in 1983.

Twelve-month revenue for reprographics and information systems rose 6 percent to $8.792 billion from $8.268 billion, it said.

The results reflect a sharp drop in insurance operations as well as a year of operating losses and fourth-quarter write-offs of $85 million from the phaseout of the company's Shugart operations, David T. Kearns, president and chief executive officer, and C. Peter McColough, chairman, said in a statement.

The company, blaming overcapacity in the industry, announced earlier this month that it would close the Sunnyvale, Calif.-based unit and take an $85 million write-off. The Shugart unit makes disk drives used to store data in office and personal computers.

* Castle & Cooke Inc. had revenue of $784.5 million for the first half of the year, up from $708.7 million in the same period a year ago. Stockholders lost $2.68 a share for the six-month period, compared with a 17-cent per share loss a year ago, when the company reported net income of $393,000.

In the second quarter, Castle & Cooke reported revenue of $324.1 million with a net loss of $51.6 million ($2.09 per share). In the same quarter a year ago, revenue stood at $306.6 million with a loss of $2.8 million (18 cents).