HW #2 evens solutions:
Check/correct with RED pen.
3a 2b−2ab2
4c2 d 2 −6
z 3 −2z 2 -4
40) p 2 − p−4 R −9
14) 7g 2 h+3g−2h 2
20) a-10 R -6
24) y 2 +9y−28 R 62
26) 2a+ 1 R 9 2
3
3
2 1
1
3
28) g − g + g R 12
2
4
30) 2z5 +4z4 +9z3 +18z2 +33z+66 R 396
12)
16)
22)
€
Turn in homework with group.
(person with the lightest color shirt)
Chapter Six
Section 6.5
Opener/Notes #3
Work on the “Opener”
problems with your group.
Opener Solutions:
1) 6ab(4a - 3b)
2) (x - 7)(x + 5)
3) (2x + 3)(x - 7)
4) (x - 7)(x + 7)
5) (a + 1)(a - 2b)
6) (4r - 3)2
Target Goal:
• Factor Polynomials (#3 and #4)
• Solve Polynomial Equations by Factoring (#5)
Factor Completely.
Example One:
• No GCF
• 3 terms (Trial and Error)
• make 2 sets of
parentheses
• split up s2
• try all possibilities for
factors of 8 (8*1 and
4*2)
• Check by Multiplying.
€
s2 −6s+8
s s






s−8 s−1
Does not check.
s−4 s−2
Does check.
Final Solution.
























Factor Completely.
Example Two:
• Factor out the GCF
• 3 terms (Trial and Error)
• make 2 sets of
parentheses
• split up a2
• try all possibilities for
factors of 6 (6*1 and
3*2)
• Check by Multiplying.
€
3a 2 +15a+18
3(a 2 +5a+6)
3a






a



3a+6 a+1
Does not check.
3a+2 a+3
Does check.
Final Solution.
























Factor Completely.
Example Three:
• Factor out the GCF.
• 2 terms (Difference of 2
Squares)
• Make 2 sets of
parentheses.
• Split up a2b2.
• Split up 121 by finding
the square root.
• Check by Multiplying.€
2a 2b 2 −242
2(a 2 b2 −121)












2 ab−11 ab+11
Does check.
Final Solution.
Factor Completely.
• Factor out the GCF.
Example Four:
• 2 terms (Difference of 2
Cubes)
• Make 2 sets of
parentheses (1 small and
1 large)
• Split up r3 into r and
r2.
• Split up 8s3 into 2s
and 4s2.
• Multiply r*2s to get
the middle term in
large parentheses. €
• Check by Multiplying.
2r 3 −16s3
3
3
2(r −8s )
2(
)(








2
2 r−2s r +2rs+4s




)
2







Final Solution.
Factor Completely.
• No GCF.
• 2 terms (Sum of 2 Cubes)
• Make 2 sets of
parentheses (1 small and
1 large)
• Split up a3b3 into ab
and a2b2.
• Split up 27 into 3 and
9.
• Multiply ab*3 to get
the middle term in €
large parentheses.
• Check by Multiplying.
Example Five:
3
3
a b +27
(
)(
)
2 2
ab+3 a b −3ab+9


















Final Solution.
Factor Completely.
• No GCF
• 3 terms (Trial and Error)
• make 2 sets of
parentheses
• split up x4
• try all possibilities for
factors of 36 (36*1, 18*2,
12*3, 9*4, and 6*6)
• Continuing factoring
the difference of 2
squares.
• Check by Multiplying.
€
Example Six:
2
4
x −13x +36







x
2
2







x
2
2







x




x−3 x+3 x−2 x+2
-9


















x -4



















Factor Completely.
• No GCF
• 4 terms (Grouping)
• Factor out 4a from the
1st 2 terms.
• Factor out 1 from the
2nd 2 terms.
• Factor out (5x - 2)
from the 2 remaining
€
terms.
Example Seven:
20ax−8a+5x−2
4a(5x−2)+1(5x−2)
(5x−2)(4a+1)
Factor Completely.
• No GCF
• 4 terms (Grouping)
• Factor out 2x2 from
the 1st 2 terms.
• Factor out -25 from
the 2nd 2 terms.
• Factor out (2a+3) from
the 2 remaining terms.
• Continue by factoring
the difference of 2
€
squares.
Example Eight:
2ax 2 +3x 2 −50a−75
x 2 2a+3 −25(2a+3)








(2a+3)(x 2 −25)
(2a+3)(x−5)(x+5)
Note:
If you can’t factor
“Prime”
Target Goal:
• Factor Polynomials (#3 and #4)
• Solve Polynomial Equations by Factoring (#5)
Homework #3
Worksheet
See board for ch.6 test date