Copyright © 2007 Pearson Education, Inc. Slide R-1

Copyright © 2007 Pearson Education, Inc. Slide R-2 Chapter R: Reference: Basic Algebraic Concepts R.1Review of Exponents and Polynomials R.2Review of Factoring R.3Review of Rational Expressions R.4Review of Negative and Rational Exponents R.5Review of Radicals

Copyright © 2007 Pearson Education, Inc. Slide R-3 R.1 Review of Exponents and Polynomials Product Rule For all positive integers m and n and every real number a,

Copyright © 2007 Pearson Education, Inc. Slide R-4 R.1 Using the Product Rule Example Find each product. (a)(b) Solution (a) (b)

Copyright © 2007 Pearson Education, Inc. Slide R-5 R.1 Review of Exponents and Polynomials Zero Exponent For any nonzero real number a, NOTE The expression 0 0 is undefined.

Copyright © 2007 Pearson Education, Inc. Slide R-6 R.1 Using the Definition of a 0 Example Evaluate each power. (a)(b)(c) Solution (a)(b) (c) since

Copyright © 2007 Pearson Education, Inc. Slide R-7 R.1 Review of Exponents and Polynomials Power Rules For all positive integers m and n and all real numbers a and b,

Copyright © 2007 Pearson Education, Inc. Slide R-8 R.1 Using the Power Rules Example Simplify each expression. (a)(b)(c) Solution (a) (b) (c)

Copyright © 2007 Pearson Education, Inc. Slide R-9 R.1 Terminology for Polynomials An algebraic expression is the result of adding, subtracting, multiplying, dividing (except by 0), or finding roots or powers of any combination of variables and constants. Examples include

Copyright © 2007 Pearson Education, Inc. Slide R-10 R.1 Terminology for Polynomials A term is the product of a real number and one or more variables raised to powers. The real number in a term is called the numerical coefficient, or just the coefficient. In the term, the coefficient is – 3.

Copyright © 2007 Pearson Education, Inc. Slide R-11 R.1 Terminology for Polynomials Like terms are terms with the same variables raised to the same powers. are like terms, are not.

Copyright © 2007 Pearson Education, Inc. Slide R-12 R.1 Terminology for Polynomials A polynomial is a term or a finite sum of terms with only nonnegative integer exponents permitted on the variables. are all polynomials.

Copyright © 2007 Pearson Education, Inc. Slide R-13 R.1 Adding and Subtracting Polynomials Polynomials are added by adding coefficients of like terms. Polynomials are subtracted by subtracting coefficients of like terms.

Copyright © 2007 Pearson Education, Inc. Slide R-14 R.1 Adding and Subtracting Polynomials Example Add or subtract, as indicated. (a) (b) Solution (a)

Copyright © 2007 Pearson Education, Inc. Slide R-15 R.1 Adding and Subtracting Polynomials Solution (b)

Copyright © 2007 Pearson Education, Inc. Slide R-16 R.1 Multiplying Polynomials The associative and distributive properties, together with the properties of exponents, can be used to multiply polynomials. Polynomials can be multiplied my multiplying each term of the first polynomial by each term of the second, then combining like terms.

Copyright © 2007 Pearson Education, Inc. Slide R-17 R.1 Multiplying Polynomials Example Multiply Solution

Copyright © 2007 Pearson Education, Inc. Slide R-18 R.1 Multiplying Polynomials A binomial is a polynomial with two terms. The FOIL method can be used to multiply two binomials. The FOIL method says to multiply the First terms, the Outside terms, the Inside terms and the Last terms, then combine like terms.

Copyright © 2007 Pearson Education, Inc. Slide R-19 R.1 Using FOIL to Multiply Two Binomials Example Find the product Solution F O I L

Copyright © 2007 Pearson Education, Inc. Slide R-20 R.1 Review of Exponents and Polynomials Special Products Product of the Sum and Difference of Two Terms Square of a Binomial

Copyright © 2007 Pearson Education, Inc. Slide R-21 R.1 Using the Special Products Example Find each product. (a)(b) Solution (a) (b)