Here we have an equation that says 4x − 7 equals 5 , and all its parts:
A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y, but can be a symbol or word.
A number on its own is called a Constant.
A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient)
Variables on their own (without a number next to them) actually have a coefficient of 1 (x is really 1x)
Sometimes a coefficient is a letter like a or b instead of a number:
An Operator is a symbol, like +, ×, etc, that shows an operation. It tells us what to do with the value(s).
A Term is either a single number or a variable, or numbers and variables multiplied together.
An Expression is a group of terms (the terms are separated by + or − signs)
So now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"
The exponent (such as the 2 in x 2 ) says how many times to use the value in a multiplication.
Exponents make it easier to write and use many multiplications
Example: y 4 z 2 is easier than y × y × y × y × z × z
Example of a Polynomial: 3x 2 + x − 2
A polynomial can have constants, variables and the exponents 0, 1, 2, 3, .
But it never has division by a variable.
There are special names for polynomials with 1, 2 or 3 terms:
Like Terms are terms whose variables (and their exponents such as the 2 in x 2 ) are the same.
In other words, terms that are "like" each other. (Note: the coefficients can be different)
Are all like terms because the variables are all xy 2