In Chapter 3, you work extensively with expressions. In this section, I discuss a few more math words that help you to break down and understand expressions better.
Variable and constant terms
Every expression is built from one or more terms, separated by either plus signs or minus signs.
Table 2-2 illustrates this concept, showing expressions with from one to four terms.
TABLE 2-2 Expressions with 1, 2, 3, and 4 Terms
| Expression | Number of Terms | Terms |
|---|---|---|
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1 |
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2 |
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3 |
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4 |
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Note that each term includes the sign that precedes it. When no sign is written explicitly, that term is positive; when it includes a minus sign, it’s a negative term.
Breaking terms into coefficient and variable
Each term in an expression can be further broken up into coefficients and variables:
The coefficient of a term is the numerical part, including the minus sign when the term is negative. It's usually listed before the variable, at the beginning of the term.
The variable part of a term is everything except the coefficient, which includes all variables and their exponents.
Identifying the coefficient and variable parts of a term is useful when you want to simplify an expression by combining like terms (as I explain in Chapter 3).
Table 2-3 shows you how to break the expression
TABLE 2-3 The Expression
| Expression | Coefficient | Variable |
|---|---|---|
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-1 |
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-8 |
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| x | 1 | x |
| 4 | 4 | None (Constant term) |
Polynomial basics
A polynomial with a single variable (x) is any expression of the following form:
This eye-glazing definition becomes a lot clearer when you see a few sample polynomials:
As you can see, each term in a polynomial is built from a variable (usually x) raised to any non-negative exponent and then multiplied by a coefficient, with terms either added or subtracted.
For clarity, polynomials are usually written in standard form, starting with the term that has the greatest exponent of x and in descending order down to the term that has the least exponent. (Note that the constant term of a polynomial technically has an exponent of 0, so it appears as the last term of a polynomial in standard form.)
Understanding the degree of a polynomial
The degree of a polynomial is determined by the exponent of its leading term — that is, the first term of the polynomial when arranged in standard form.
The leading term of a polynomial is instrumental in naming the degree of that polynomial. Table 2-4 provides examples of the four most common polynomials.
TABLE 2-4 Polynomials of Degree 1, 2, 3, and 4
| Polynomial | Degree | Name of Degree |
|---|---|---|
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1 | Linear |
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