Get out your binders!
Today’s Objectives:
You will be able to solve quadratics by
factoring using GCF.
You will be able to solve quadratics by
factoring when 𝑎 = 1.
Warm Up
Using the given function below…
a)
b)
c)
Find the y-intercept, the axis of
symmetry, and the vertex
Make a table
Graph the function
d)
e)
f)
𝟐
State whether the function has a
minimum or maximum
Find the value of the min/max
Find the roots
𝒇 𝒙 = 𝒙 − 𝟑𝒙 + 𝟐
4.3 Solve by Factoring
Factor
A factor is a number that is
multiplied with another number to
get a product.
𝟔 × 𝟑 = 𝟏𝟖
FACTOR
FACTOR
Factor
A factor is a number that is
multiplied with another number to
get a product.
Find the factors of −20:
Think: which TWO numbers can be multiplied
together to get a product of −20?
Greatest Common Factor
We’re here!
Greatest Common Factor
Find numbers and variables that can
be factored out of every term in the
expression—"factoring" means
"dividing out and putting in front of the
parentheses".
Nothing "disappears" when you
factor; things merely get rearranged.
Greatest Common Factor
You will use the GCF to …
1. FACTOR equations, and
2. SOLVE equations
We will begin with FACTORING.
Greatest Common Factor
Factor the following equations.
1. 7𝑥 − 7
2
2. 3𝑥 + 9
3. −𝑥 5 − 5𝑥 2
2
4. −16𝑥 + 8𝑥
5. 9𝑥 2 𝑦 6 + 3𝑥 3 𝑦 4
You Try!
FACTOR the following equations.
4
1. 12𝑥 + 6𝑥
2.
2
−2𝑦
+ 4𝑦
Zero Property
The zero property is used to solve for 𝒙.
If multiple terms multiplied together equal
zero, you can separate each term, set each
equal to 0, and solve.
𝟐𝒙 𝟒𝒙 + 𝟖 = 𝟎
𝒙−𝟗 𝒙−𝟓 =𝟎
𝟓𝒙 𝟒𝒙 + 𝟏 𝒙 − 𝟔 = 𝟎
Solving with GCF
Solve by factoring the GCF
FIRST and then using the zero
property.
𝟐
𝟏𝟐𝒚 − 𝟐𝒚 = 𝟎
Solving with GCF
SOLVE the following equations.
2
1. 20𝑥 + 15𝑥 = 0
2
2. − 9𝑧 − 3𝑧 = 0
2
3. 14𝑥 + 7𝑥 = 0
You Try!!!
SOLVE the following equations.
2
1. −2𝑥 + 4𝑥 = 0
2
2. 4𝑦 + 16𝑦 = 0
Factoring when a=1
We’re here!
Factoring when a=1
Factoring a trinomial is the
opposite of FOIL.
(𝒙 − 𝟒)(𝒙 + 𝟓)
Factoring when a=1
𝟐
1 𝒙 − 𝟐𝒙 − 𝟏𝟓
Remember that this is where 𝒂 is!
And when you don’t see a number, it is 1!
Factoring when a=1
Factoring when 𝒂 = 𝟏,
1. set up two sets
of parenthesis
with an 𝑥 in
each,
2. find two factors
of c that add up
to equal b, then
3. write each factor
in a parenthesis.
𝟐
𝒙 − 𝟐𝒙 − 𝟏𝟓
Factoring when a=1
FACTOR the following.
2
1. 𝑥 − 15𝑥 + 36
2.
2
𝑥
+ 7𝑥 + 12
3.
2
𝑥
− 𝑥 − 30
You Try!
FACTOR the following.
2
1. 𝑥 − 8𝑥 + 15
2
2. 𝑥 − 2𝑥 − 35
Solving with a=1
Solve by factoring the equation
FIRST and then using the zero
property.
𝟐
𝒙 + 𝟔𝒙 + 𝟖 = 𝟎
Solving when a=1
SOLVE the following.
2
1. 𝑥 + 5𝑥 + 6 = 0
2.
2
𝑥
2
− 9𝑥 + 20 = 0
3. 𝑥 − 4𝑥 − 21 = 0
You Try!
SOLVE the following.
2
1. 𝑥 + 5𝑥 − 24 = 0
2.
2
𝑥
− 11𝑥 + 30 = 0
QUICK REVIEW
SOLVE the following.
1.
2
9𝑥
2.
2
𝑥
+ 3𝑥 = 0
− 4𝑥 + 4 = 0
2
3. 𝑥 − 2𝑥 − 15 = 0
4.
2
9𝑥
+ 3𝑥 = 0
Ticket Out The Door
On a 3x5 Card answer the following.
What numbers can replace the ? to
make this trinomial factorable.
𝟐
𝒙
+ ? 𝒙 + 𝟏𝟐 = 𝟎
Solve.
𝟐
𝟑𝒙
+ 𝟏𝟐𝒙 = 𝟎
Homework
4.3 Worksheet—
Day 1 #’s 1-15