Solving
Quadratic
Equations
Before we learn to solve
quadratic equations, we need
to remember an important
property!
Zero Product Property
If ab = 0, then a = 0 or b = 0.
a and b are real numbers (“factors”)
Examples:
a2= 0, then a = 0
3b = 0 then b = 0
a(a + 2) = 0, then a = 0 or a
+2 = 0
SO…
a = 0 or a = -2.
Solving Quadratics
Let’s learn how to solve quadratics by
factoring the greatest common factor!
When solving by factoring the
GCF, the quadratic equation
will look a certain way!
The quadratic equation will have two
types of terms: A quadratic term
and a linear term.
ax  bx  0
2
Examples
4w  2w
2
5t  3t  0
2
OK, so how do we solve quadratic
equations that look this way?!!!
Solve by factoring GCF
Solve
4w  2w
2
Step 1: Make one side zero, if not already.
4w  2w  0
Step 2: Factor out the GCF.
2w(2w  1)  0
Step 3: Set each factor to zero and solve
for the variable.
2w  1  0
2
2w  0
w0
OR
1
w
2
Let’s Practice!
You Try It!
Solve 5t  3t  0
2
t (5t  3)  0
Factor
the GCF!
t  0 or 5t  3  0
3
t  0 or t  
5
YOU DID IT!
Hooray!!!
THE END