## Intermediate Algebra: Connecting Concepts through Application

$\text{Number of terms: } 3 \\\text{1st term: } 4m^7np^3 \text{ (variable term; coefficient is$4$)} \\\text{2nd term: } 24m^5n^4p^3 \text{ (variable term; coefficient is$24$)} \\\text{3rd term: } 14 \text{ (constant term)}$
$\bf{\text{Solution Outline:}}$ Use the definition of an algebraic term, a constant term, a variable term, and the coefficient of a term. $\bf{\text{Solution Details:}}$ Algebraic terms are constants and variables that are separated by a plus or minus sign. Constant terms are terms without any variable. Terms that contain a variable are called variable terms. The constant that goes with the variable term is called its coefficient. Using the definitions above, the given expression, $4m^7np^3+24m^5n^4p^3+14 ,$ has the following characteristics: \begin{array}{l}\require{cancel} \text{Number of terms: } 3 \\\text{1st term: } 4m^7np^3 \text{ (variable term; coefficient is $4$)} \\\text{2nd term: } 24m^5n^4p^3 \text{ (variable term; coefficient is $24$)} \\\text{3rd term: } 14 \text{ (constant term)} .\end{array}