Stuff You Should Know
About Exponents and Polynomials

Rules of Exponents

Exponent of 0	a0 = 1	where a ≠ 0
Exponent of 1	a1 = a
Negative Exponent	a-n = 1/an	where a ≠ 0
Product Rule	am·an = am+n
Quotient Rule	am/an = am-n	where a ≠ 0
Power Rule	(am)n = am·n
Product to a Power	(a·b)n = an·bn
Quotient to a Positive Power	(a/b)n = an/bn	where b ≠ 0
Quotient to a Negative Power	(a/b)-n = (b/a)n	where a ≠ 0 and b ≠ 0
Scientific Notation	M · 10n	where 1 < M < 10

Polynomials

1. A monomial is an expression of the form axⁿ.
2. A polynomial is an expression containing the sum and/or difference of one (1) or more monomials.
3. A binomial is an expression containing the sum and/or difference of two (2) monomials.
4. A trinomial is an expression containing the sum and/or difference of three (3) monomials.
5. The degree of a term is the exponent of the variable.
6. The degree of a polynomial is the greatest degree of its terms.
7. Only like terms of a polynomial can be added or subtracted.
8. To multiply two polynomials, multiply each term of the first polynomial by each term of the second polynomial, then combine like terms.
9. To multiply two binomials, you may also use the FOIL method:
1. Multiply the First Terms
2. Multiply the Outside Terms
3. Multiply the Inside Terms
4. Multiply the Last Terms