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In the expression 5x + 3, the coefficient is 5.
7 is the coefficient of the variable d
4ac + 2ad + 2bc +bd = 2a*(2c + d) + b*(2c + d) = (2c + d)*(2a + b)
The coefficient of 3+7d is 7
In the expression 2x, the 2 is the coefficient. It tells you how many of the x you need.