Slide 2:
The Principle of Zero Products assures us that if a product is
equal to 0 then one or both of the factors of that product is
equal to 0. For example:
If ab = 0 then either a = 0 or b = 0. So… if (x + 3)(x – 2) = 0 then
either x + 3 = 0 or x – 2 = 0!!
Slide 3:
In order to solve quadratics by factoring, you will need to follow
the steps below: Make sure the equation is equal to zero to start.
Factor the quadratic.
Set each factor equal to zero (uses the Principle of Zero
Products).
4. Solve each equation.
Slide 4:
Solve x2 – 9 = 0. Factor: (x + 3)(x – 3) = 0 Apply the Principle of Zero Products.
x + 3 = 0 or x – 3 = 0 Solve. X = -3 or x = 3
Slide 5:
Solve x2 – 4x – 12 = 0 Factor: (x – 6)( x + 2) = 0 X – 6 = 0 or x + 2 = 0 (Principle of Zero Products) X = 6 or x = -2
Slide 6:
Solve 2x2 + x = 10 First, you need to set the equation equal to 0 so…
subtract 10 from both sides… 2x2 + x = 10
-10 -10
2x2 + x – 10 = 0 Now factor: (2x + 5)(x – 2) = 0 2x + 5 = 0 or x – 2 = 0 2x = -5
X = -5/2 X = 2
Slide 7:
Solve 4x2 = 8 Get equation to equal 0 – subtract 8… 4x2 = 8
-8 -8
4x2 – 8 = 0 Factor: (GCF) 4x (x – 2) = 0 4x = 0 or x – 2 = 0 x = 0 or x = 2