Example (MML ref 13.1: 1, 2, 3): Factor each
polynomial by factoring out the GCF.
a) 5x2 + 10x + 15
b) 5x3 + 10x2 + 15x
c) 5x4 + 10x3 + 15x2
d) 10xy + 5y
e) x3 - x2
f) 4x2 - 6x
g) 4xy + 8x2y
h) 25x2 - 30y2
i) - 2x3y - 6x2y - 10xy
Question: Should we have factored out -2 in problem i?
• Rule: In general is the term with the highest degree (the leading term) is
negative, we will factor out a negative GCF. Otherwise, we’ll factor out a
positive GCF .
• If the leading term is negative and has a coefficient of -1, we will
factor out a -1.
Example: Factor out the GCF.
a) -3x + 6y
b) -4x2 - 8x + 4
c) -x - 5
Example (MML ref 12.1: 4, 5):
What is the GCF of 3(x - 1) + y(x - 1)?
Can we factor 3(x - 1) + y(x - 1) by factoring out the GCF?
Can we factor x(x - 4) - 3(x - 4) by factoring out the GCF?
To factor by grouping: 1. Find the GCF of the first two terms and factor it out.
2. Find the GCF of the second two terms and factor it out, making sure that what
is left matches what was left in step 1. In this step, you may have to factor a
“1” or “-1” as a place holder.
3. “What was left” becomes the common factor and can now be factored. Factor
that out. This becomes the first final factor.
4. The second final factor is the combination of what remains .
ax + ay + bx + by
Example (MML ref 12.1: 6, 7, 8, 9, 10): Factor by
a) 2x + 2y + x2 + xy
b) 2y + 8 + xy + 4x
c) 8y2 - 12y + 10y - 15
d) 15a6 - 25a3 - 6a3 + 10
e) 8x2 - 4x + 2x -
f) 3x2 + 6x - x - 2
Multiple Choice Practice Questions.
1) Factor completely: 36a2b2 - 9ab
B. 9ab(4ab - 1)
C. 9ab(4a2b2 - 1)
D. 3ab(12ab - 3)
2) Factor completely: 6x2 - 6xy - 5x + 5y
A. (6x - 5)(x + y)
B. (6x - y)(x + 5)
C. (6x - 5)(x - y)
D. (6x - y)(x - 5)
12x2y - 42x2 - 4y + 14 Hint: Remember to factor out a GCF first!
The GCF is the largest number that divides evenly
into every number in the set.
Finding the GCF of a set of variables
The GCF is the product of the smallest powers of
the common factors.
Factoring out the GCF of a polynomial
To factor out the GCF, find the GCF and rewrite
the polynomial as the product of two ex pressions : the GCF and the
polynomial with each term having the GCF divided out.
Factoring by grouping
To factor a four term polynomial by grouping,
factor a common factor out of each pair of terms. That should leave a
binomial in common . Factor out that binomial and combine what’s left.
sure to work My Math Lab Homework section 13.1.
Optional Reinforcement Activities
Work the concept extensions at the top of page 953.
92) not factored
93) not factored
59, 61, 62, 65, 67, 69, 71, 73
For next time: Read pages 955 - 958 in your textbook.