Do Now 3/15/10Do Now 3/15/10

►Take out your HW from Friday.Take out your HW from Friday. Text p. 603, #4-40 multiples of 4Text p. 603, #4-40 multiples of 4

►Copy HW in your planner.Copy HW in your planner. Text p. 610, #4 – 40 multiples of 4Text p. 610, #4 – 40 multiples of 4

► In your notebook, list your thought In your notebook, list your thought process (questions you ask yourself) process (questions you ask yourself) when you are given an expression when you are given an expression to factor.to factor. (**Hint: think of the sections we have covered so far (**Hint: think of the sections we have covered so far in Chapter 9)in Chapter 9)

HomeworkHomeworkText p. 603, #4-40 multiples of 4Text p. 603, #4-40 multiples of 4

► 4) (n + 8)(n – 8) 4) (n + 8)(n – 8) ► 8) 9(5x + 4y)(5x – 8) 9(5x + 4y)(5x –

4y)4y)► 12) (3t – 2)²12) (3t – 2)²► 16) (2f – 9)²16) (2f – 9)²► 20) 5(3r – 4s)²20) 5(3r – 4s)²► 24) A24) A► 28) +4/3, -4/328) +4/3, -4/3► 32) +6, -6 32) +6, -6 ► 36) +1/6, -1/636) +1/6, -1/6► 40) +12, -1240) +12, -12

ObjectiveObjective

►SWBAT factor polynomials completelySWBAT factor polynomials completely

Factoring Polynomials Factoring Polynomials ReviewReview

► (9.5) (9.5) Factor x² + bx + cFactor x² + bx + c

► (9.6) (9.6) Factor ax² + bx + cFactor ax² + bx + c

► (9.7) (9.7) Factor special productsFactor special products

x² – 7x – 30 x² – 7x – 30

(x – 10)(x + 3)(x – 10)(x + 3)

3z² + z – 143z² + z – 14

(3z + 7)(z – 2)(3z + 7)(z – 2)

9z² – 36z + 369z² – 36z + 36

(3z – 6)²(3z – 6)²

72z² – 9872z² – 98

2(6z – 7)(6z + 7)2(6z – 7)(6z + 7)

Perfect square trinomialPerfect square trinomial Difference of two squaresDifference of two squares

►Factor out a common binomial-Factor out a common binomial- 2x(x + 4) – 3(x + 4)2x(x + 4) – 3(x + 4)

►Factor by grouping-Factor by grouping- xx³ + 3x² + 5x + 15³ + 3x² + 5x + 15

Section 9.8 “Factor Polynomials Section 9.8 “Factor Polynomials Completely”Completely”

2x(x + 4) – 3(x + 4)2x(x + 4) – 3(x + 4)

Factor out a common binomialFactor out a common binomial

Factor out the common binomialFactor out the common binomial

2x2x(x + 4)(x + 4) – 3 – 3(x + 4)(x + 4)= = (x + 4)(x + 4) (2x – 3)(2x – 3)

4x²(x – 3) + 5(x – 3)4x²(x – 3) + 5(x – 3)Factor out the common binomialFactor out the common binomial

4x²4x²(x – 3)(x – 3) + 5 + 5(x – 3)(x – 3)= = (x – 3)(x – 3) (4x² + 5)(4x² + 5)

7y(y – 2) + 3(2 – y)7y(y – 2) + 3(2 – y)

Factor out a common binomialFactor out a common binomial

The binomials y – 2 and 2 – y are opposites. The binomials y – 2 and 2 – y are opposites. Factor out -1 from 3(2 – y) to obtain -3(y – 2). Factor out -1 from 3(2 – y) to obtain -3(y – 2).

Factor out the common binomialFactor out the common binomial

7y7y(y – 2)(y – 2) – 3 – 3(y – 2)(y – 2) = = (y – 2)(y – 2) (7y – 3)(7y – 3)

7y7y(y – 2)(y – 2) – 3 – 3(y – 2)(y – 2)

2y²(y – 4) – 6(4 – y)2y²(y – 4) – 6(4 – y)

Factor out a common binomial…Try It OutFactor out a common binomial…Try It Out

The binomials y – 4 and 4 – y are opposites. The binomials y – 4 and 4 – y are opposites. Factor out -1 from -6(4 – y) to obtain 6(y – 4). Factor out -1 from -6(4 – y) to obtain 6(y – 4).

Factor out the common binomialFactor out the common binomial

2y²2y²(y – 4)(y – 4) + 6 + 6(y – 4)(y – 4)= = (y – 4)(y – 4) (2y² + 6)(2y² + 6)

2y²2y²(y – 4)(y – 4) + 6 + 6(y – 4)(y – 4)

x³ + 3x² + 5x + 15x³ + 3x² + 5x + 15Factor by groupingFactor by grouping

Group terms into binomials and look to factor out a common binomial.Group terms into binomials and look to factor out a common binomial.

Factor out Factor out each groupeach group

x²x²(x + 3) (x + 3) + 5+ 5(x + 3)(x + 3)= = (x + 3)(x + 3) (x² + 5)(x² + 5)

(x³ + 3x²) + (5x + 15)(x³ + 3x²) + (5x + 15)

(x + 3)(x + 3)x²x² (x + 3)(x + 3)+ 5+ 5

Factor out the common binomialFactor out the common binomial

x³ – 6 + 2x – 3x²x³ – 6 + 2x – 3x²Factor by grouping…Try It OutFactor by grouping…Try It Out

Group terms into binomials and look to factor out a common binomial.Group terms into binomials and look to factor out a common binomial.

Factor out Factor out each groupeach group

x²x²(x – 3) (x – 3) + 2+ 2(x – 3)(x – 3) = = (x – 3)(x – 3) (x² + 2)(x² + 2)

(x³ – 3x²) + (2x – 6)(x³ – 3x²) + (2x – 6)

(x – 3)(x – 3)x²x² (x – 3)(x – 3)+ 2+ 2

Factor out the common binomialFactor out the common binomial

Reorder polynomial with degree of powers decreasing from left to right.

x³ x³ – 3x² – 3x² + 2x + 2x – 6– 6

Factoring Polynomials CompletelyFactoring Polynomials Completely

► (1) (1) Factor out greatest common monomial factor.Factor out greatest common monomial factor.

► (2) (2) Look for difference of two squares or perfect Look for difference of two squares or perfect square trinomial.square trinomial.

► (3) (3) Factor a trinomial of the form axFactor a trinomial of the form ax² + bx + c into ² + bx + c into binomial factors.binomial factors.

► (4) (4) Factor a polynomial with four terms by Factor a polynomial with four terms by grouping.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)

HomeworkHomework►Text p. 610, #4 – 40 multiples of 4Text p. 610, #4 – 40 multiples of 4

HomeworkHomework Punchline worksheet 13.11 “Why Did the Boy Punchline worksheet 13.11 “Why Did the Boy Sheep Plunge Off a Cliff While Chasing the Girl Sheep Plunge Off a Cliff While Chasing the Girl

Sheep?”Sheep?”SET 1SET 1► a) (a + 4)(a + 5)a) (a + 4)(a + 5)► b) (a – 4)(a + 6)b) (a – 4)(a + 6)► c) (a + 8)(a – 8)c) (a + 8)(a – 8)► d) (a – 1)(5a + 4)d) (a – 1)(5a + 4)

► e) (5a + 2)(5a + 2e) (5a + 2)(5a + 2))SET 2SET 2► a) (u – 3)(2u – 5)a) (u – 3)(2u – 5)► b) (7 + 4u)(7 – 4u)b) (7 + 4u)(7 – 4u)► c) (u – 7)(2u + 5)c) (u – 7)(2u + 5)► d) (u – 2)(7u + 2)d) (u – 2)(7u + 2)► e) (7u – 4)(7u – 4)e) (7u – 4)(7u – 4)

SET 3SET 3► a) (k + 3)(8k + 1)a) (k + 3)(8k + 1)► b) (2k + 3)(4k – 1)b) (2k + 3)(4k – 1)► c) (k – 1)(4k – 11)c) (k – 1)(4k – 11)► d) (2k + 11)(2k – 11)d) (2k + 11)(2k – 11)► e) (k – 2)(11k + 8)e) (k – 2)(11k + 8)

SET 4SET 4► a) (9xa) (9x² + y² + y)(9x)(9x² – y)² – y)► b) (x – 5y)(3x – 8y)b) (x – 5y)(3x – 8y)► c) (9x + y)(9x + y)c) (9x + y)(9x + y)► d) (3x – y)(3x + 8y)d) (3x – y)(3x + 8y)► e) (x + 4y)(9x + 2y)e) (x + 4y)(9x + 2y)

““HE DIDN’T SEE THE EWE TURN”HE DIDN’T SEE THE EWE TURN”