1. Lesson #6 Factor by Grouping & Difference of Squares Factoring Polynomials

2. Recall from last yesterday, that it is possible to factor out a monomial or even a higher order polynomial. eg. 1 2x 3 y 2 – 4x 2 y 2 =2x 2 y 2 (x– 2) x(y + 3) - 2(y +3) =(y + 3) (x – 2) Greatest Common Factor Binomial eg. 2 Factor c(b + 2) + 7(b + 2) =(b + 2) (c + 7) 3(x + y) – 5(x + y) =(x + y)(3-5) = -2(x + y)

3. eg. 3 On many occasions, the binomial factor may not be obvious and require some manipulation. ab – 3a + 2b - 6 =a(b – 3)+ 2(b – 3) (a + 2) Factor to get one Common binomial =(b – 3) This is called group factoring. eg. 4 Factor 6ab + 3b – 4a - 2 =3b (2a + 1)- 2 (2a + 1) (3b - 2) =(2a + 1) 2xy + 15 - 6x -5y =2xy - 6x – 5y + 15 =2x (y - 3)- 5 (y - 3) (2x - 5)=(y - 3)

4. Sometimes we cannot group factor. eg. 5 What do we do? factor Consider (2x – 3)(2x + 3) = 4x 2 + 6x - 6x - 9 = 4x 2 - 9 We call these conjugates eg. 6 Factor these difference of squares = (b - 1)(b + 1)= (3a - 5)(3a + 5) = (x - y)(x + y)

5. = (7p -6q)(7p + 6q)Not a difference of squares = (x 2 – y 2 ) (x 2 + y 2 ) eg. 7 = 2 (x 2 - 25) =2(x - 5)(x+5) =y 6 – 100x 2 =(y 3 –10x)(y 3 +10x) = (x–(x+4)) (x+(x+4)) = -4 (2x+4) = -8(x+2) Perfect squares follow the general form = (x – y)(x+y)(x 2 +y 2 )

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