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Objective # 16 Factoring Polynomials - 1st Step: Factor Out Common Factors Material: page 134 to 140 Homework: worksheet are expressions that are being added or subtracted Terms Examples: 3x3y2z 3x + 4y x2 - 3x + 5 one term two terms three terms monomial binomial trinomial are expressions that are being multiplied Factors Examples: Factoring (3)(4) two factors (5)(x + 3) two factors (4x)(x - 2) two factors (x - 1)(2x + 3) two factors 3 and 4 5 and x + 3 4x and x - 2 x - 1 and 2x + 3 is a process used to find all the factors that were multiplied to give a polynomial expression. Three methods for factoring polynomials: 1st Factor out common factors 2nd Factor the binomial called the difference of two squares into the product of its conjugate pairs. 3rd Factor trinomials into the product of two binomials. Example 1: Multiple each of the following factors: a) (3)(x + 2) b) (-2)(5x - 1) c) - (4 - x2) d) (x)(x + 3) e) (3x)(4 - 2x) f) (-5x)(2x - 3) g) (x)(x2 + 4x - 3) h) (2x)(1 + 5x - 3x3) i) (-4x2)(3x -2) Example 2: Factor out the common factors (if any) in each of the following polynomials: a) 3x + 9 b) 12x - 16 c) 24 + 16x - 8x2 d) x2 + 4x e) 3x3 - x2 f) 5x + 3x2 + 2x3 g) 4x2 + 12x h) 8x3 - 28x i) 15x3 + 6x2 - 9x Factoring Polynomials - 1st Step: Factor Out Common Factors Worksheet 1. Multiple each of the following factors: a) -(x - 1) b) (4)(7x - 2) c) (-3)(2x2 + 5x -1) d) (x)(2x + 3) e) (7x)(x - 2) f) (-2x)(4x2 - 3x + 9) g) (x2)(1 - 2x) h) (5x3)(3 + 2x) i) (-x2)(2 - x + 3x2) j) (3x)(4 - 2x2) k) (-x)(-5x - 2) l) -(3x2 + 7x - 4) 2. Factor out the common factors (if any) in each of the following polynomials: a) 7x - 14 b) 10 - 15x c) 24x2 + 36x - 12 d) 2x2 - 3x e) x3 + x 2 f) 2x3 - x2 + 5x g) 12x + 8 h) 5x2 - 20x i) 2x3 + 6x2 - 8x j) 6x2 + 15 k) 4x3 - 9x2 l) 9x3 - 15x2 + 21x m) 18x4 + 27x2 n) 4x4 + 6x3 - 8x2 + 10x o) 18x - 12x2 p) (3x)(x + 4) + (2)(x + 4) q) (2x)(3x - 1) - (5)(3x - 1) r) (x)(2x + 1) + (2x +1)