What Is the Difference Between a Term & a Factor in Algebra?

Learning the difference between a term and a factor is crucial for understanding more advanced concepts in algebra.
••• Jupiterimages/Photos.com/Getty Images

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.

Terms

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.

Factors

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.

Related Articles

How to Identify a Numerical Coefficient of a Term
How to Factor Higher Exponents
How to Factor Polynomials Step-by-Step
The Foil Method With Fractions
How to Find Terms in an Algebra Expression
How to Factor Binomial Cubes
Algebra Rules for Beginners
How to Factorise a Quadratic Expression
How to Factorise in Math
How to Factor Polynomials in Factor Four Terms
How to Factor Polynomials With Fractions
How to Factor Monomials
How to Factor Algebraic Expressions Containing Fractional...
Algebra 1 Compared to Algebra 2
How to Do Linear Equations in Math
How to Factor a Perfect Cube
How to Factor Polynomials With 4 Terms
How to Use the AC Method for Factoring
How to Factor Expressions in Algebra
How to Solve Rational Expression Equations

Dont Go!

We Have More Great Sciencing Articles!