Factoring and the Factor Theorem Hints to determine each type

Difference of Perfect Squares Simple Trinomial Complex Trinomial Factor by Grouping Two TermsThree TermsFour Terms Examine the Number of Terms Each term is a perfect square separated by a “-” sign Is of the form x 2 +bx +c Is of the form ax 2 +bx +c, where a≠0. Always look for a Greatest Common Factor Group in pairs of terms Should be able to factor twice Finally, check each factor to see if it can be factored further. Sum/Diff of Cubes

Sum and Difference of Cubes Sum of cubes: x 3 +y 3 = (x+y)(x 2 -xy+y 2 ) Difference of cubes: x 3 -y 3 = (x-y)(x 2 +xy+y 2 ) Eg. x Eg. 8x y 3 = (x-3)(x 2 +3x+9) =(2x 2 +5y)(4x 4 -10x 2 y+25y 2 )

Factor Theorem A polynomial P(x) has x – b as a factor if and only if P(b) = 0. Factor: P(x) = 2x 3 – 5x 2 – 4x + 3 Since P(-1) = 0, therefore x + 1 is a factor. Try factors of +/-3 and +/- 3/2 to get the root Repeat the process to find other factors or use long division to find remaining factors P(x) = (x+1)(2x-1)(x-3)

Factor Completely 1.x 2 – 3x y 2 -6y x 2 +4x x 2 – xy – x +y 5.t x a b 12 8.x 3 – x 2 – 16x x 3 + 5x 2 – 2x - 24