Elementary Algebra A review of concepts and computational skills Chapters 5-7

Polynomials  Polynomial—term, degree, constant, coefficient, like terms  Monomial, binomial, trinomial  Adding and subtracting polynomials– look for like terms

Multiplying Polynomials  Multiplying Polynomials by monomials  Multiplying Binomials– FOIL method  Special Products

Dividing Polynomials  Dividing polynomials by monomials  Dividing polynomials by binomials (long division)

Properties of Exponents  a m x a n = a m+n  a m / a n = a m-n  a 0 = 1  (a m ) n = a mn  (ab) n = a n b n  (a/b) n = a n /b n

Negative Exponents and Scientific Notation  a –n = 1/a n  1/a -n = a n  (a/b) -n = (b/a) n  Scientific Notation: Used for very large or very small numbers: a x 10 n where 1<a<10 and n is an integer

Factoring  Prime, composite numbers; prime factorization  GCF- greatest common factor  Factoring special products  Factor by grouping

More Factoring  Factoring 2 nd degree trinomials for a = 1  Factoring other 2 nd degree trinomials  Sum or difference of 2 cubes  Solving quadratics by factoring

Rational Expressions  Rational Expression: a ratio of 2 polynomials with denominator not equal to zero  Evaluating  Finding values x cannot be (domain)  Reducing

Multiply and Divide Rational Expressions  Multiply—simplify first, then multiply  Divide– flip second expression, then simplify and multiply

Add and Subtract Rational Expressions  Find the LCD– least common denominator  Convert denominators  Add or subtract, then simplify

More Rational Expressions  Complex fractions  Solving equations with rational expressions