Which of the following is a monomial?

CONCEPT — A monomial is an algebraic expression consisting of exactly one term.

Its variables have non-negative integer exponents, and a numerical coefficient may multiply them.

APPLICATION — Count terms by locating addition or subtraction signs that separate parts of an expression. The expression 4x2 has one term, whereas a + 6 has two terms and a + 6 + c has three terms.

CONTRAST —

• 4x2: one term, with coefficient 4 and exponent 2 on x.

• a + 6: two terms separated by addition.

• a + 6 + c: three terms separated by addition.

• More than one of the above: this would require at least two one-term expressions, but the term counts are 1, 2, and 3.

• None of the above: this would require no one-term expression, but one displayed expression has term count 1.

CROSS-CHECK — Removing the coefficient 4 leaves x2, still a single variable-power term; no addition or subtraction separates another term.

RESULT — Therefore, the monomial is 4x2.