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Algebra comes with a whole new set of terminology to learn. One of those terminologies is that of a monomial. A monomial is a polynomial that has only one term. So what is a polynomial?
A polynomial is an expression of variables and coefficients. The variables and coefficients involve mathematical operations that include addition, subtraction, multiplication and non-negative integer-exponents.
So, what is a variable? A variable is an alphabetic character used to represent a number that is not known. For example: x + y. The “x” and “y” are variables used in place of numeric numbers that are not known.
What is a coefficient? A coefficient is a known number that is linked to a variable. For example: 7x + 3y = 29. In this example the 7 and the 3 are coefficients because they are linked to variables. The 29 is a constant number and is not a coefficient because it is not linked to a variable.
Whenever a coefficient is linked to a variable, it is understood that the operation will be multiplied. Again looking at the above example, we know that 7 times an unknown number plus 3 times an unknown number will equal 29. When replacing a variable with a number, the number is placed within parentheses. Now let’s look at the solution to our problem as it should be written out.
7(2) + 3(5) = 29
7 x 2 = 14
3 x 5 = 15
14 + 15 = 29
x = 2
y = 5