1. Factoring

2. Page 80: Factoring GCF 3x2 + 18x + 9 =3(x2 + 6x + 3) 4k4 + 18k3 – 6k2
Mistake on the homework page 80
#14) answer is P the problem is messed up
=3(X2 + 2X + 1)

3. Page 97: Factor by Grouping
X2 + 3X + XK + 3K
M2 + MN – 3M – 3N
=X(X + 3) + K(X + 3)
=(X + K) (X + 3) or (X + 3) (X + K)
=M(M + N) – 3(M + N)
=(M – 3) (M + N) or (M + N) (M – 3)

4. Page 84 top left: Multiply
(a + 5) (a – 5)
(a2 – 6) (a2 + 6)
= a2 – 5a + 5a – 25
= a2 – 25
= a4 + 6a2 – 6a2 – 36
= a4 – 36

5. Page 84: Factoring Difference of Squares
36x2 – 121y2
4a16 – 225
What about x2 + 25? Does it factor?
= (6x – 11y) (6x + 11y)
= (2a8 – 15) (2a8 + 15)
Try (x + 5) (x + 5) or (x + 5) (x – 5) or (x – 5) (x – 5)
Conclusion: Sum of Squares is NOT factorable.
We call it prime.

6. Page 90: Quick Factor N2 + 6N + 5 N2 + 2N – 15 A2 – 29AB + 100B2
Factors of +5
Sum of +6
= (N + 5) (N + 1)
Factors of -15
Diff of +2
= (N – 3) (N + 5)
1* *5
Factors of +100
Sum of -29
= (A – 4B) (A – 25B)
1* *50 4* *10
Factors of -32
Diff of -14
= (A + 2B) (A – 16B)
1* * *8

7. Factoring: Sum & Difference of Cubes
A3 – B3 = (A – B)(A2 + AB + B2)
A3 + B3 = (A + B)(A2 – AB + B2)
1000X3 + 27
64X3 – 1
= (10X + 3) (100X2 – 30X + 9)
= (4X – 1) (16X2 + 4X + 1)

8. Page 91: Long Factor 3x2 + 7x + 2 8u2 – 9u + 1 7n2 – 13n – 2
Factors of +6
Sum of +7
= 3x2 + 1x + 6x + 2
1* *3
=x(3x + 1) + 2(3x + 1)
= (x + 2)(3x + 1)
Factors of +8
Sum of -9
= 8u2 – 1u – 8u + 1
1* *4
=u(8u – 1) – 1(8u – 1)
= (u – 1)(8u – 1)
Factors of -14
Diff of -13
= 7n2 + 1n – 14n – 2
1* *7
=n(7n + 1) – 2(7n + 1)
= (n – 2)(7n + 1)

9. Page 93: Factoring, All Mixed Up
Binomials:
Take out GCF
Check for Diff of Squares, Diff/Sum of Cubes
Trinomials:
Check for Quick Factor (coef in front = 1)
Check for Long Factor (coef in front ≠ 1)

10. Page 94: All Mixed Up with GCF
3x2 – 15x + 18
60m3 + 54m2 – 6m
= 3(x2 – 5x + 6)
Factors of +6
Sum of -5
1* *3
= 3(x – 2) (x – 3)
= 6m(10m2 – 9m – 1)
Factors of -10
Diff of -9
1* *5
= 6m(10m2 + 1m – 10m – 1)
= 6m[ m(10m + 1) – 1(10m + 1) ]
= 6m (m – 1) (10m + 1)

11. Page 93: Factoring, All Mixed Up
Binomials:
Take out GCF
Check for Diff of Squares & Diff/Sum of Cubes
A2 – B2 = (A – B)(A +B)
A3 – B3 = (A – B)(A2 + AB + B2)
A3 + B3 = (A + B)(A2 – AB + B2)
Trinomials:
Check for Quick Factor (coef in front = 1)
Check for Long Factor (coef in front ≠ 1)