1. Do Now 2/27/19 Take out your HW from last night.
Punchline worksheet 13.11
Copy HW in your planner.
Text p. 407, #4-36 evens
In your notebook, list your thought process (questions you ask yourself) when you are given an expression to factor. Then factor the 5 expressions to the right.
3x² + 6x
x² + 4x + 4
16x² – 49
x² – 7x + 10
3x² – 5x – 2

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 x² + bx + c into binomial factors.
(4) Factor a trinomial of the form ax² + bx + c into binomial factors.
(5) 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)
x² – 7x + 10
= (x – 2)(x – 5)
3x² – 5x – 2
= (3x + 1)(x – 2)
-4x² + x + x³ - 4

3. “HE DIDN’T SEE THE EWE TURN”
Homework Punchline worksheet “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”

4. Learning Goal Learning Target SWBAT factor polynomials completely
SWBAT simplify, factor, and solve polynomial expressions and equations
Learning Target
SWBAT factor polynomials completely

5. Factoring Polynomials Review
(7.4) Greatest Common Factor
(7.5) Factor x² + bx + c
(7.6) Factor ax² + bx + c
(7.7) Factor special products
6x² – 12x
6x(x – 2)
x² – 7x – 30
(x – 10)(x + 3)
3z² + z – 14
(3z + 7)(z – 2)
Perfect square trinomial
Difference of two squares
72z² – 98
z² – 12z + 36
(z – 6)²
2(6z – 7)(6z + 7)

6. Section 7.8 “Factor Polynomials Completely”
Factor out a common binomial-
2x(x + 4) – 3(x + 4)
Factor by grouping-
x³ + 3x² + 5x + 15

7. 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)

8. 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)

9. 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)
= 2(y² + 3)
(y – 4)

10. 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)

11. 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)

12. Problem Solving (16 – w) (w) (w + 4)
A box has a volume of 768 cubic inches and all three sides are different lengths. The dimensions of the box are shown. Find the width, length, and height.
Volume = length x width x height
(16 – w)
(w)
(w + 4)
Substitute the possible solutions to see which dimensions work out.
w = 12
w = 8 8 4 8 12 12 16
w = -8
w = 8
w = 12
Volume = 12 x 16 x 4
Can’t have negative width

13. 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 x² + bx + c into binomial factors.
(4) Factor a trinomial of the form ax² + bx + c into binomial factors.
(5) Factor a polynomial with four terms by grouping.
4x² + 10x
= 2x(2x + 5)
x² + 4x + 4
= (x + 2)(x + 2)
16x² – 49
= (4x + 7)(4x – 7)
x² – 7x + 10
= (x – 2)(x – 5)
3x² – 5x – 2
= (3x + 1)(x – 2)
-4x² + x + x³ - 4
= (x² + 1)(x – 4)

14. Homework
Text p. 407, #4-36 evens