Download 9.4 Day 1 R

Algebra Part 3
Unit 9
Name____________________________
Date________________
Warm-up:
Simplify:
1. (x + 7)(x – 7)
2. (x2 - 5x + 1) (x – 1)
3. (x + 3)2
4. (x – 2)(x – 2)
Guided Notes
9.4 Day 1 Solve Polynomial Equations in Factored Form
Finding the
GREATEST COMMON FACTOR
*It is important to learn how to factor polynomials. This will allow us to find solutions to
polynomial equations later on.
The first thing we look for when factoring is the Greatest Common Factor. We can
practice finding GCFs with the help of FACTOR TREES
Ex 1:
36
Guided Practice:
Find the GCF of:
1)
48
and
24
56
2)
60
and
80
Sometimes we have to find the GCF between two terms that have common variables. The
GCF is how many of that variable each term has in
Ex 2: Find the GCF between x6y3z10 and
COMMON.
x3 y 7 z
GCF: __________________________
Guided Practice:
1) a10b6c7
a12b10c2
and
GCF:____________________________
Now lets apply finding GCFs to polynomials. The Greatest Common Factor is the
monomial with an integer coefficient that divides evenly into each term. Here’s how it
works:
Ex. 3: Factor 6x – 4
The GCF, or in other words the biggest number that goes into 6 and 4 is
2.
So, we
FACTOR OUT or DIVIDE OUT a 2 from each term.
So,
6x + 4
=
2(
)
You can think of this as doing the distributive property in
REVERSE.
Guided Practice:
1) Factor 4y + 12
2) Factor 16p – 32
Finally, let’s factor polynomials that have a GCF that includes both numbers AND
variables.
Ex. 4 Factor 4x4 + 24x3
The GCF is _____, so the answer is 4x3 (x + 6)
Guided Practice: Factor
1) 6y3 – 15y6
2) 13g5 + 39g6