Transcript Elementary Algebra - Utah State University

Elementary Algebra
A review of concepts and
computational skills
Chapters 5-7
Polynomials
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Polynomial—term, degree, constant,
coefficient, like terms
Monomial, binomial, trinomial
Adding and subtracting
polynomials– look for like terms
Multiplying Polynomials
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Multiplying Polynomials by
monomials
Multiplying Binomials– FOIL method
Special Products
Dividing Polynomials
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Dividing polynomials by monomials
Dividing polynomials by binomials
(long division)
Properties of Exponents
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am x an = am+n
am / an = am-n
a0 = 1
(am)n = amn
(ab)n = an bn
(a/b)n = an/bn
Negative Exponents and Scientific
Notation
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a–n = 1/an
1/a-n = an
(a/b)-n = (b/a)n
Scientific Notation: Used for very
large or very small numbers: a x
10n where 1<a<10 and n is an
integer
Factoring
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Prime, composite numbers; prime
factorization
GCF- greatest common factor
Factoring special products
Factor by grouping
More Factoring
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Factoring 2nd degree trinomials for a
=1
Factoring other 2nd degree
trinomials
Sum or difference of 2 cubes
Solving quadratics by factoring
Rational Expressions
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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
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Multiply—simplify first, then
multiply
Divide– flip second expression, then
simplify and multiply
Add and Subtract Rational Expressions
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Find the LCD– least common
denominator
Convert denominators
Add or subtract, then simplify
More Rational Expressions
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Complex fractions
Solving equations with rational
expressions