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Methods of Factoring Copyright © 2008 Pearson Addison-Wesley. All rights reserved. R-73 1.Greatest Common Factor(gcf) – the product of each prime factor to its highest power. Useful for any number of terms. 2.Factoring by grouping – factor common factors for grouping of two terms at a time. Used for 4 terms. 3.Factoring patterns: a.Difference of Two Squares: 2 x 2 – y 2 = (x + y)( x - y) b.Perfect Squares Trinomial: 2 x 2 – 2xy + y 2 = ( x - y) 2 2 x 2 + 2xy + y 2 = ( x + y) 2 2 4.Trinomials - ax 2 + bx + c i.a = 1 ii.a ≠ 1

R.5 Example 1(a) Writing Rational Expressions in Lowest Terms (page 44) Copyright © 2008 Pearson Addison-Wesley. All rights reserved. R-74 Write the rational expression in lowest terms. (a) Factor. Divide out the common factor.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. R-75 Write the rational expression in lowest terms. (b) R.5 Example 1(b) Writing Rational Expressions in Lowest Terms (page 44) Factor. Multiply numerator and denominator by –1. Divide out the common factor.

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. R-78 R.5 Example 2(c) Multiplying or Dividing Rational Expressions (page 45) Divide. Multiply by the reciprocal of the divisor. Factor. Multiply, then divide out common factors.

Rules for Exponents 1.Product Rule: a m. a n = a m+n 2.Quotient Rule:a m /a n = a m-n 3.Power Rules:(ab) m = a m b m (a/b) m = a m /b m (a m ) n = a mn 4.Negative Exponent: a -m = 1/a m 5.Zero Exponent: a 0 = 1 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. R-85

Copyright © 2008 Pearson Addison-Wesley. All rights reserved. R-93 R.6 Example 5 Using the Definition of a m/n (cont.) Evaluate each expression. (d) (e) (f) is not a real number because is not a real number.