Function : A function is a mapping in which every element in one set is mapped to exactly one element of a second set. Most often the mapping is described using a rule. For example the function $f(x)=x+1$ maps 2 to 3 and -1 to 0.

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.

Arithmetic progression : A sequence of numbers $x_1, x_2, x_3,\ldots$ is called arithmetic progression if the difference between any two consecutive numbers in the sequence is the same. $1,3,5,7,\ldots$ and $2,5,8,11,\ldots$ are examples of arithmetic progressions. The sum of a finite arithmetic progression can be calculated by using that the last element plus the first element equals the second to last plus the second element and so on. For example $1+2+\ldots+99+100$ $=(1+100)+(2+99)+(3+98)+\ldots+(50+51)$ $=50\cdot 101=5050$

Consecutive numbers : Two integers are consecutive if you get the second integer by adding 1 to the first integer.

Number : A number $x$ is a mathematical symbol representing a quantity.