Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.

Comparing coefficients : Comparing coefficients means to check if all the coefficients of two polynomials coincide. For example to check if a polynomial equals zero you can equivalently check if all of its coefficients are zero.

Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Equation : An equation is a mathematical statement in which two expressions are written with an equal sign in between. A solution of an equation is a set of variables that makes the statement a true statement.

Solution : A solution to an equation is a choice of variables that when substituted into the equation results in a true statement.