Do Now 3/15/10 Take out your HW from Friday. Copy HW in your planner. Text p. 603, #4-40 multiples of 4 Copy HW in your planner. Text p. 610, #4 – 40 multiples of 4 In your notebook, list your thought process (questions you ask yourself) when you are given an expression to factor. (**Hint: think of the sections we have covered so far in Chapter 9)

Homework Text p. 603, #4-40 multiples of 4 4) (n + 8)(n – 8) 8) 9(5x + 4y)(5x – 4y) 12) (3t – 2)² 16) (2f – 9)² 20) 5(3r – 4s)² 24) A 28) +4/3, -4/3 32) +6, -6 36) +1/6, -1/6 40) +12, -12

Objective SWBAT factor polynomials completely

Factoring Polynomials Review (9.5) Factor x² + bx + c (9.6) Factor ax² + bx + c (9.7) Factor special products x² – 7x – 30 (x – 10)(x + 3) 3z² + z – 14 (3z + 7)(z – 2) Perfect square trinomial Difference of two squares 72z² – 98 9z² – 36z + 36 (3z – 6)² 2(6z – 7)(6z + 7)

Section 9.8 “Factor Polynomials Completely” Factor out a common binomial- 2x(x + 4) – 3(x + 4) Factor by grouping- x³ + 3x² + 5x + 15

2x(x + 4) – 3(x + 4) 4x²(x – 3) + 5(x – 3) 2x(x + 4) – 3(x + 4) Factor out a common binomial 2x(x + 4) – 3(x + 4) Factor out the common binomial 2x(x + 4) – 3(x + 4) = (x + 4) (2x – 3) 4x²(x – 3) + 5(x – 3) Factor out the common binomial 4x²(x – 3) + 5(x – 3) = (x – 3) (4x² + 5)

7y(y – 2) + 3(2 – y) 7y(y – 2) – 3(y – 2) 7y(y – 2) – 3(y – 2) Factor out a common binomial 7y(y – 2) + 3(2 – y) The binomials y – 2 and 2 – y are opposites. Factor out -1 from 3(2 – y) to obtain -3(y – 2). 7y(y – 2) – 3(y – 2) Factor out the common binomial 7y(y – 2) – 3(y – 2) = (y – 2) (7y – 3)

2y²(y – 4) – 6(4 – y) 2y²(y – 4) + 6(y – 4) 2y²(y – 4) + 6(y – 4) Factor out a common binomial…Try It Out 2y²(y – 4) – 6(4 – y) The binomials y – 4 and 4 – y are opposites. Factor out -1 from -6(4 – y) to obtain 6(y – 4). 2y²(y – 4) + 6(y – 4) Factor out the common binomial 2y²(y – 4) + 6(y – 4) = (y – 4) (2y² + 6)

x³ + 3x² + 5x + 15 (x³ + 3x²) + (5x + 15) x² (x + 3) + 5 (x + 3) Factor by grouping x³ + 3x² + 5x + 15 Group terms into binomials and look to factor out a common binomial. (x³ + 3x²) + (5x + 15) x² (x + 3) + 5 (x + 3) Factor out each group Factor out the common binomial x²(x + 3) + 5(x + 3) = (x + 3) (x² + 5)

x³ – 3x² + 2x – 6 x³ – 6 + 2x – 3x² (x³ – 3x²) + (2x – 6) x² (x – 3) Factor by grouping…Try It Out Reorder polynomial with degree of powers decreasing from left to right. x³ – 3x² + 2x – 6 x³ – 6 + 2x – 3x² Group terms into binomials and look to factor out a common binomial. (x³ – 3x²) + (2x – 6) x² (x – 3) + 2 (x – 3) Factor out each group Factor out the common binomial x²(x – 3) + 2(x – 3) = (x – 3) (x² + 2)

Factoring Polynomials Completely (1) Factor out greatest common monomial factor. (2) Look for difference of two squares or perfect square trinomial. (3) Factor a trinomial of the form ax² + bx + c into binomial factors. (4) Factor a polynomial with four terms by grouping. 3x² + 6x = 3x(x + 2) x² + 4x + 4 = (x + 2)(x + 2) 16x² – 49 = (4x + 7)(4x – 7) 3x² – 5x – 2 = (3x + 1)(x – 2) -4x² + x + x³ - 4 = (x² + 1)(x – 4)

Homework Text p. 610, #4 – 40 multiples of 4

“HE DIDN’T SEE THE EWE TURN” Homework Punchline worksheet 13.11 “Why Did the Boy Sheep Plunge Off a Cliff While Chasing the Girl Sheep?” SET 1 a) (a + 4)(a + 5) b) (a – 4)(a + 6) c) (a + 8)(a – 8) d) (a – 1)(5a + 4) e) (5a + 2)(5a + 2) SET 3 a) (k + 3)(8k + 1) b) (2k + 3)(4k – 1) c) (k – 1)(4k – 11) d) (2k + 11)(2k – 11) e) (k – 2)(11k + 8) SET 2 a) (u – 3)(2u – 5) b) (7 + 4u)(7 – 4u) c) (u – 7)(2u + 5) d) (u – 2)(7u + 2) e) (7u – 4)(7u – 4) SET 4 a) (9x² + y)(9x² – y) b) (x – 5y)(3x – 8y) c) (9x + y)(9x + y) d) (3x – y)(3x + 8y) e) (x + 4y)(9x + 2y) “HE DIDN’T SEE THE EWE TURN”