Many students confuse the notion of the "term" and the "factor" in algebra, even with the clear differences between them. The confusion comes from how the same constant, variable or expression can be a term or a factor, depending on the operation involved. Differentiating between the two requires a look at the individual function.
In a problem, constants, variables or expressions that appear in addition or subtraction are called terms. Expressions involve constants and variables in one of the four primary operations (addition, subtraction, multiplication or division). For example, in the equation y = 3x(x + 2) - 5, "y" and "5" are terms. While "x + 2" does involve addition, it's not a term. Before simplification, however, that equation would have read y = 3x^2 + 6x - 5; all four items are terms.
Using the same example from the prior section, 3x^2 + 6x includes two terms, but you can also factor 3x out of both of them. So you can turn that into (3x)(x + 2). These two expressions multiply together; constants, variables and expressions involved in multiplication are called factors. So 3x and x + 2 are both factors in that equation.
A Factor or Two Terms?
The use of parentheses around the x + 2 indicates that it is an expression involved in multiplication. The only reason that a "+" sign still is present is that x and 2 are not like terms, and so no further simplification is possible. If they were both constants, or both multiples of x, it would be possible to combine them and remove the sign.
Importance of Factoring
Looking at strings of terms that are added or subtracted and figuring out when to break the string down and factor out certain constants, variables or expressions is a skill that is vital for algebra and higher math levels. Factoring allows you to find solutions to complex polynomials.
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