Do Now 3/15/10
► Take
out your HW from Friday.
 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)
► 8)
► 12)
► 16)
► 20)
► 24)
► 28)
► 32)
► 36)
► 40)
(n + 8)(n – 8)
9(5x + 4y)(5x – 4y)
(3t – 2)²
(2f – 9)²
5(3r – 4s)²
A
+4/3, -4/3
+6, -6
+1/6, -1/6
+12, -12
Objective
► SWBAT
factor polynomials completely
Factoring Polynomials
Review
► (9.5)
Factor x² + bx + c
x² – 7x – 30
(x – 10)(x + 3)
► (9.6)
Factor ax² + bx + c
3z² + z – 14
(3z + 7)(z – 2)
► (9.7)
Factor special products
Perfect square trinomial
9z² – 36z + 36
(3z – 6)²
Difference of two squares
72z² – 98
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
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)
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)
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)
Factor by grouping
x³ + 3x² + 5x + 15
Group terms into binomials and look to factor out a common binomial.
(x³ + 3x²) + (5x + 15)
Factor out
each group
x² (x + 3) + 5 (x + 3)
Factor out the common binomial
x²(x + 3) + 5(x + 3) = (x + 3)(x² + 5)
Factor by grouping…Try It Out
x³ – 3x²
6++
2x2x
– 3x²
–6
Reorder polynomial
with degree of
powers decreasing
from left to right.
Group terms into binomials and look to factor out a common binomial.
(x³ – 3x²) + (2x – 6)
Factor out
each group
x² (x – 3) + 2 (x – 3)
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.
3x² + 6x
►
= 3x(x + 2)
(2) Look for difference of two squares or perfect square
trinomial.
x² + 4x + 4
16x² – 49
►
= (x + 2)(x + 2)
= (4x + 7)(4x – 7)
(3) Factor a trinomial of the form ax² + bx + c into
binomial factors.
3x² – 5x – 2 = (3x + 1)(x – 2)
►
(4) Factor a polynomial with four terms by grouping.
-4x² + x + x³ - 4
= (x² + 1)(x – 4)
Homework
►Text
p. 610, #4 – 40 multiples of 4
Homework
Punchline worksheet 13.11 “Why Did the Boy Sheep
Plunge Off a Cliff While Chasing the Girl Sheep?”
SET 1
SET 3
►
►
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 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)
►
►
►
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 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”