Factoring Polynomials by Grouping

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Presentation transcript:

Factoring Polynomials by Grouping Section 5.4(d) Factoring Polynomials by Grouping

Group the terms with common variables and factor V. Factor by Grouping (4-terms) ( ) ( ) a2x - b2x + a2y -b2y Both terms have an x Both terms have a y x(a2 - b2) + y(a2 - b2) Both terms have (a2 - b2) (a2 - b2)( ) x + y Can you go farther?

(cont.) Difference of 2 squares (a2 - b2)( x + y ) (a + b)(a - b)(x + y)

* * * * Factor by grouping: 4x2 + 7x + 3 a.) 4•3 = 12 12 x 1 6 x 2 Factors of 12 * * a.) 4•3 = 12 12 x 1 6 x 2 4 x 3 12 + 1 = 13 b.) Add the factors 6 + 2 = 8 Why? 4 + 3 = 7 Look for factors that add to 7 Why?

( ) ( ) (cont.) Now rearrange the original trinomial 4x2 + 7x + 3 Separate the middle term (7x) into 2 pieces: 4x and 3x 4x2 + 7x + 3 4x2 + 4x + 3x + 3 Why? 4 + 3 = 7 c.) Now group the first 2 terms and the last 2 terms 4x + 3x = 7x ( ) ( ) 4x2 + 4x + 3x + 3

( ) ( ) ( ) ( 4x + 3 ) (cont.) 4x2 + 4x + 3x + 3 ( ) ( ) 4x2 + 4x + 3x + 3 d.) Look for a GCF (greatest common factor) in each term 4x(x + 1) + 3(x + 1) e.) Look for a GCF in each term again ( ) 4x(x + 1) + 3(x + 1) (x + 1) ( 4x + 3 ) (x + 1)(4x + 3) Done

(cont.) Check by “foiling” (distributing) (x + 1)(4x + 3) = 4x2 + 3x + 4x + 3 = 4x2 + 7x + 3

29.) Factor by grouping

30.) Factor by grouping

31.) Factor by grouping

V. Factor trinomial by any method 32.) Factor

33.) Factor

34.) Factor

Homework Page Problems # 16, and 40 - 48