f;a~tors and &r~tast ~omraon Factors

See pages481-486,Fa~torin9 Using tha Pistributiva l~ropartyConcept Summary¯ Find the greatest common factor and then use the Distributive Property.¯ With four or more termS, try factor~g by grouping.Factoring by Grouping: ax + bx + ay + lry = x(a + b) + y(a + b) = (a +~Factoring can be used to solve some equations.Zero Product Property: For any rea! numbers a and b, if ab = 0, theneither a = 0, b = 0, or both a and b equal zero.Factor 2x 2 - 3xz - 2xy + 3!~z.2X 2 -- 3XZ -- 2xy + 3~d z = ( 2x2 Group terms with common factors.- 3xz) + (-2xy + 3yz)Factor out the GCF from each grouping.= x(2x - 3z) - y(2x - 3z)Factor out the common factor ~x - 3z.=- (X -- y)(2x -- 3z)olynomiaL See Examples 1 and 2 on pages 481 and 482.¯, 27. 4rs + 12ps + 2mr j- 6mP~l~ ~(; ~~-k .3. e,~’~3 ~ our solutions. See~amples2and~°npages~and~"olve eac~ equahon. Check y30. (3n + 8)(2n - o) =. v ¯~a~torin9 Trinom~als:See ~ages Concept Su~ma~489-494. ¯ Factorb~g x ~ + bx + c: F~d m and n whose sum is b an~ whose product is~en write x 2 + bx + c as (x + m)(x + n).Solve a 2 - 3a - 4 = 0. Then check the solutions.a~-3a-4=0(a+~)(a-4)=0a+l=0 or a -4=0a = -1 a=4Original equationFactor.Zero Product PropertySolve each equation.The solUtiOn set is {-1, 4}.See Examples ! 4 on pages 490 and 491. l’ ~ ¯ ~ trinomi al - ¯ "~ ’’-~Exercises Factor.each ~,’"2 ,~ "a.4(-~oV’~.’~ 34" ~b2+Sb-6 ~ ~)~2 ,2 + 7u + 12 Q-~ ~’~J 33. x - 7~ - ~ ~2 " ~ ~ m 2 -- 4ran = 32n~9 r 2 ~u’" ~ ~ ~35. _. )