1. 8.2 Factoring using the GCF & the Distributive Property
Algebra 1
8.2 Factoring using the GCF & the Distributive Property
Factor: 29xy – 3x
Ask yourself: What is Common in both parts? 29xy & 3x
The x is common so you factor it out.
Which is like “backwards or reverse distribution”.
x (29y – 3)
Factor this one: 3y2 + 12
The 3 is common in both parts…therefore
3(y2 + 4)

2. More Factoring Factor: 11x + 44x2y 11x(1 + 4xy) Factor: 16a + 4b
Factor: 3p2q – 9pq2 + 36pq
3pq(p – 3q + 12)

3. Factoring by Grouping
Using the distributive property to factor polynomials having four or more terms.
(3mx + 2my) + (3kx + 2ky)
What’s common in the first 2? m
What’s common in the second 2? k
Therefore, m(3x + 2y) + k(3x + 2y)
Take a look at the “big picture” – what’s the same?
(3x + 2y) – therefore we can factor it out
(3x + 2y)(m + k)

4. More factoring 2ax + 6xc + ba + 3bc 2x(a + 3c) + b(a + 3c)
(a + 3c)(2x + b)
2ax + ab + 6cx + 3bc
a(2x + b) + 3c(2x + b)
(2x + b)(a + 3c)

5. Using the Additive Inverse Property
Factor: c – 2cd + 8d – 4
c(1 - 2d) + 4(2d – 1)
Notice that the parentheses are slightly different (just opposite signs)
Therefore you need to factor out a -1 from one of the parentheses
c (-1)(-1 + 2d) + 4(2d – 1)
-c (2d – 1) + 4(2d – 1)
(2d – 1)(-c + 4)

6. Solve equations in factored form using the Zero Product Property
Set each parentheses equal to zero and solve.
(d + 5)(d – 3) = 0
d + 5 = 0 d – 3 = 0
d = d = 3
Solution Set {-5,3}
(2x + 4)(3x – 6) = 0
2x + 4 = 0 3x – 6 = 0
2x = x = 6
x = -2 x = 2
Solution Set {-2,2}
Roots: The solutions of an equation.

7. Add another step! y2 = 6y Rewrite so it = 0 y2 – 6y = 0
GCF y(y – 6) = 0
Set each = 0 y = 0 y – 6 = 0
Get y by itself (solve for y) y = 0 y = 6
Solution Set {0,6}

8. Homework #57
p , 32, 38